On erev Shabbos of Chanukah when it is impossible to light at the regular set time by Chazal, the candles must be lit earlier. Starting from plag hamincha, 1 1/4 hours before shkia, one can already light with a brocha and fulfill his mitzvah for the coming night.
Many try to daven mincha early on erev Shabbos Chanukah. There are two reasons brought for this minhag. Shaar Hatziyun in 679-7 brings a Pri Megadim that by lighting after plag we are declaring that this is a time for doing mitzvahs for the coming night. [This is similar to the custom some have of accepting Shabbos early during the summer months and davening Maariv after plag, even though it is still daytime]. If so, it would seem contradictory to daven mincha during this time being that mincha is a mitzvah from the previous day. The second reason is brought by the Shaarei Teshuva that mincha is in place of the daily afternoon offering in the Bais Hamikdash and Chanukah candles are a remembrance of the miracle which occurred with the candles of the Bais Hamikdash.The candles were lit after the afternoon offering was brought. Therefore, mincha should be davened before the candles are lit.
If however one cannot organize their day to catch an early minyan, it is better to daven later with a minyan after lighting candles rather than early without a minyan.
Adopted from the shiurim of Ha Rav Tzvi Hyman, Mier Yashiva, Jerusalem