On Friday night of Chanukah, Halacha mandates that the Chanukah candles should be lit before the Shabbat candles. But what is the Halacha if the Shabbat candles were mistakenly lit first, such as if the wife forgot to wait for the husband to light Chanukah candles? If the sun has yet to set, may the Chanukah candles be lit even after the Shabbat candles were lit?
The answer is that one may light the Chanukah candles in such a case. The husband may certainly light the candles, since he did not light the Shabbat candles and thus has clearly yet to accept Shabbat. And even the wife, who lit the Shabbat candles, may be involved in lighting the Chanukah candles, according to the practice of the Sephardim that women do not accept Shabbat with the lighting of the Shabbat candles.
Thus, so long as the sun has yet to set, one may light the Chanukah candles even after the Shabbat candles have been lit, since in practice the lighting of the Shabbat candles does not constitute an acceptance of Shabbat.
Another question that occasionally arises on Friday night of Chanukah is whether one should relight the Chanukah candles if they blow out soon after they are lit, assuming, once again, that the sun has not set. Strictly speaking, a Halachic principle dictates, "Kavta, Ein Zakuk La" – if the Chanukah candles are extinguished, one need not relight them. However, it is nevertheless commendable for one to relight them. On Friday night, therefore, if one has ample time before sundown, he should preferably relight the Chanukah candles, without a Beracha. If, however, the candles blew out just several minutes before sundown, one should not rekindle them. Since he bears no obligation to relight according to the strict Halacha, it is preferable to refrain from doing so rather than run the risk of lighting candles after Shabbat has begun.
Finally, the question was asked whether one may make personal use of the Chanukah candles on Friday night until sundown. Generally, Halacha forbids deriving any kind of personal benefit from the Chanukah candles, such as reading by their light. One might have argued that on Friday night, when we must light early, before the actual Mitzva takes effect, this prohibition against personal use from the candles perhaps does not apply until sundown. The Peri Megadim (Rabbi Yosef Ben Meir Teomim, 1727-1792), however, rules that the prohibition applies even before sundown on Friday night. The fact that we recite the Berachot when lighting the Chanukah candles on Friday night proves that we do, indeed, consider the time for the Mitzva to have arrived, even though we light before sundown. Therefore, the prohibition against deriving benefit from the Chanukah candles takes effect immediately with the lighting.
Summary: On Friday night of Chanukah, the Chanukah candles must be lit before the Shabbat candles. If, however, the Shabbat candles were mistakenly lit first, the husband may still light the Chanukah candles until sundown, and even the wife may participate in the lighting, according to the Sephardic practice that women do not accept Shabbat with lighting the Shabbat candles. If the Chanukah candles blow out before sundown on Friday night, it is proper to relight them – without a Beracha –unless only several minutes remain until sundown. One may not derive benefit from the light of the Chanukah candles, even on Friday night, when they are lit early.
