Let us examine whether or not a person who is away from home on Chanuka should light his own menora. There are three issues that need to be addressed here:

1. Reasons for lighting neiros Chanuka away from home.

2. When the husband is away from home.

3. When the husband is in a later time zone than his home.

1. Reasons for lighting neiros Chanuka away from home

a) Mehadrin min hamehadrin - Beautifying the mitzva

The basic mitzva of neiros Chanuka, Chanuka candles, is to kindle one ner, candle, for one's entire household. However the universal minhag, custom, is to follow the mehadrin min hamehadrin - those who seek to beautify the mitzvos to the highest degree. The Ashkenazic interpretation of mehadrin min hamehadrin is that every family member lights their own menora, kindling an additional candle each night 1. Since the minhag of mehadrin min hamehadrin applies equally whether one is at home or not 2, one should go beyond the minimum requirement and light when they are away from home. This applies to male family members. Women are not included in this minhag 3.

b) Hallel v'hoda'ah - Thanks and praise to Hashem

There is another reason why a person away from home can justify lighting their own menora. The mitzva of neiros Chanuka is a two-fold obligation. One aspect of the mitzva is on the household - lighting in every home to publicise the miracle. Family members who are away from home at the time of lighting fulfil this part of their obligation even though they are not physically present. However, there is a second requirement on each individual of hallel v'hoda'ah, to thank and praise Hashem for the miracle. It was due to this personal obligation that Chazal, the Sages, instituted the blessings She'asa nissim and Shehechiyanu 4. Therefore even regarding the basic requirement, it should be incumbent upon any family member not present for the household hadlaka, to light a menora to fulfil their individual obligation.

2. When the husband is away from home

It is generally considered mehadrin min hamehadrin for family members to light their own menora after the head of the house has lit and fulfilled the mitzva (see 1a above). There is, however an exception to this rule. When a husband is away and the wife lights at home for the household, the husband is also included in her mitzva. He cannot rely on mehadrin min hamehadrin to light with the brachos. This is based on the principal of ishto k'gufo - a husband and wife are considered to be one entity for this mitzva. In effect it is as if he has personally lit 5. But if he stipulates that he does not wish to fulfil the mitzva through his wife's agency, one might think that ishto k'gufo no longer applies and that he could light for himself. However the Poskim debate whether or not a husband can release himself from his wife's lighting in this manner. Therefore even if he would specify that he does not wish to fulfil the mitzva with her, he still cannot light with the brachos 6.

What then of his personal obligation of hallel v'hoda'ah? Perhaps he should light Chanuka candles in order to recite the brachos and express his gratitude and praise to Hashem. However, there is a difference of opinion amongst the Rishonim as to whether the husband's individual obligation of hallel v'hoda'ah is automatically fulfilled along with his household obligation when his family lights 7. Lighting with the brachos could entail a possibility of a bracha l'vatala, reciting a bracha in vain.

The halacha is that he is included in his family's lighting and there is no personal obligation in this case 8.

One, who wants to be stringent and follow all opinions, can do one of the following:

a) Light before one's wife will kindle the candles at home. He can then recite the brachos as well (This applies whether he is in the same time zone as his wife or an earlier time zone).9

b) If he wants to light later than his wife will, he should ask someone to include him with their brachos. After he hears the brachos he can light his own menora 10.

c) Lastly, he can be mishtateif b'pruta - become a partner in his host's lighting by paying him part of the cost of the oil or candles and then listen to his host's brachos.11

3. When the husband is in a later time zone than his home

Our discussion until now has assumed that the husband and wife are in the same time zone. Does the halacha change if the husband is staying in a later time zone than his home (e.g., if one lives in Australia and travels to Eretz Yisrael or the United States)? Some Poskim say that in this case the husband does not fulfil his mitzva when his wife lights at home. This is because when his wife lights in Australia, it is still not Chanuka where he is staying (or on the second night in Australia, it is still the first day of Chanuka in Eretz Yisrael or the United States). According to this opinion he would be obligated to light and recite the brachos.12

However there are poskim who maintain that he still fulfils the mitzva with his wife's lighting at home even though it is not time for him to light Chanuka candles yet. They understand that the main obligation is on the household like mezuza and it is irrelevant where the individual is 13.

Since there is a doubt as to whether he has fulfilled the mitzva, he must light candles where he is staying, though he cannot recite the brachos. Ideally he should hear the brachos from someone else, or he should be mishtateif b'pruta with someone else and hear their brachos 14.

FOOTNOTES

1. Orach Chaim (O.C.) 671:2 with Rema. The common practice today is to light mehadrin min hamehadrin. See Rema 675:3 and Mishna Berura (M.B.) 677:1.
2. (See however Mishbetzos Zahav 677:1, mentioned end of note 5.)
3. Even though women are also obligated to light Chanuka candles (O.C. 675:3), a wife does not light because we apply the principle of 'ishto k'gufo, a husband and wife are considered to be one entity, M.B. 671:9, 675:9 and Sha'ar Ha'tzion 675:10. The prevalent custom is that all girls in one's household also do not light. See Chidushei Chasam Sofer, Shabbos 23a, Salmas Chaim 259; Moadim U'zmanim 2:132.
4. The S'fas Emes Shabbos 21b asks whether there is a mitzva on every individual to light which one fulfils with the lighting of the head of the household, or whether there is only one mitzva on the entire household. See also P'nei Yehoshua there. However, the Bach 676 (also cited by the Magen Avraham 676:2 and Machatzis Hashekel 676:1) states that there are two obligations; one on the household and another on each individual. Many Achronim, later commentaries, mention this idea. This is why one who is unable to light makes a bracha when seeing Chanuka lights, Birchas haRo'eh. See M.B. 676:6 and Sha'ar Ha'tzion 676:9. See also the Piskei Teshuvos 676:3 discussion of this issue.
5. Both the Taz (677:1) and Magen Avraham 677:9 quote the Terumas Hadeshen No. 101 that the principle of mehadrin min hamehadrin can be applied to a husband and wife when they are in two different locations. Accordingly, the husband may still light Chanuka candles even though his wife is lighting at home. However the Mishna Berura 677:15 brings the Maharil that stipulates that this is only permissible if the husband has in mind that he does not want to fulfil his obligation with his wife's lighting. See the Magen Abraham, ibid.
The Taz writes that the Beis Yosef and Maharshal go further. They say that one cannot stipulate that he does not wish to fulfil his mitzva with his wife. The Eliyahu Rabba 671:3, cited by the Mishbetzos Zahav 677:1, explains that the rule of ishto k'gufo supersedes mehadrin min hamehadrin, ie., he always fulfils his mitzva with his wife's lighting. Therefore the husband cannot light away from home. This is also explained in the M.B. 677:16.
The Mishbetzos Zahav, ibid, also offers another explanation. He writes that it is only considered mehadrin when one lights in one's home. When one is a guest in another home, his candles would not be regarded as hiddur, an enhancement of the mitzva, see there. See also next halacha.
6. The M.B. 677:15, 16; see Taz end of previous note. One might ask "can one's wife have in mind that she does not want her husband to fulfil his mitzva when she lights?" (Usually when one fulfils his obligation through someone else, if either one intends that the recipient shall not fulfil his mitzva, the mitzva is invalidated for the recipient.) Rabbi Y. Roth shlita in Mai Chanuka, Piskei Halachos No. 21 writes that in all likelihood there is no difference between the husband and wife. Together they are only obligated in one mitzva.
7. According to the Rashba, when candles are kindled in one's house, one is no longer obligated in the personal mitzva l'hallel u'l'hodos, to thank Hashem and praise Him for the miracle. According to Rashi and the Mordechai however, even though the family lit the menora he still has his personal obligation l'hallel u'l'hodos. See the Shulchan Aruch O.C. 666:3, who follows the Rashba's view and the Rema 677:3, who follows the Mordechai.
8. See M.B. 676:6. See also O.C. 677:3 with M.B. 677:14-16.
9. M.B. 677:16.
10 Ibid.
11. Sha'ar HaTzion 676:10.
12. See B'Tzeil HaChachma 5:102, No.5, and Ohelecha B'amisecha 39:15; Be'er Moshe Vol.7, p.223, No. 2. Ta'arich Yisrael 22:16 writes that Dayan Y.Y. Fischer shlita and Rabbi Chaim Kanievsky shlita also lean towards this view. Taarich Yisrael 22:18 quotes Rabbi Ch. P. Sheinberg shlita that this is true even in regard to the family obligation. We have to look at the individual first. The Minchas Yitzchak 7:47 concludes that he is in doubt over this issue. However, he tends more towards the opinion that one cannot fulfil the mitzva with the family hadlaka (lighting).
13. The Minchas Yitzchak ibid (see end of previous note) writes that from the Gemara and Poskim's discussion, it seems the halacha does not change because of one's location. This is also implied in the M.B. 677:2, who writes that one fulfils his obligation when his wife lights in his house even though he is far away from home. It seems that even if he is in a different time zone, he still fulfils his obligation.
This is also the ruling of HaGaon Rabbi Shlomo Zalman Auerbach zt'l, Mivakshei Torah No. 18 (Kislev 5756) Siman 2. He writes that the main obligation is on the family. (This can be compared to mezuza. There is an obligation for a mezuza to be affixed to one's home; it is not incumbent on the individual to affix a mezuza. He adds however that there is a difference between mezuza and Chanuka lighting. If someone else puts up a mezuza in one's home, the mitzva is fulfilled even if the owner did not appoint him as a shaliach, an agent. On Chanuka however, a non-family member cannot light for the family unless he was designated as a shaliach. There is still an element of a personal obligation on Chanuka.)
This is also the opinion of the Mishneh Halachos vol. 2 O.C. 539 and Kinyan Torah 4:82. Also, the Kuntras U'Vlechtecha Vaderech brings a ruling of Rabbi Nissim Karelitz shlita. He says that an American girl visiting Eretz Yisrael for Chanuka does not have to light and can rely on her family lighting in the United States, even though there is a big time difference between the two countries (However a boy would have to light according to the minhag to light mehadrin). It should be noted, that according to the opinions mentioned in the previous note, a girl who is away from home, should be mishtateif b'pruta.
14.Minchas Yitzchak ibid. However one who wants to recite the brachos has whom to rely on. (The suggestion of the M.B. for one to light before his wife is not applicable since it will be Chanuka for her first.)