At my shul, the first maariv minyan on Chanukah is after teitz hachocavim (5:15, in Eretz Yisroel). It takes a couple minutes until there are ten people, and when ten people arrived some members wanted to daven first and light in shul after the minyan. (Everyone at this minyan lights first at home.) Is there any precedent for this?
The Rama 671:7 seems to say that even if people are in a hurry that the chazzan should light before maariv:
אם רוצים למהר להתפלל לאחר שבירך הש" ץ והדליק אחד מהן יוכל השמש להדליק הנשארים והשליח צבור יתפלל. [מהרי"ל]:
If [the prayer leader] wants to quickly pray right away after [he] has recited the benedictions and kindled one of them, the synagogue attendant may kindle the rest, and the prayer leader may pray. (Jacob ben Moses Moelin)
However, the reasons for lighting before maariv brought by the Mishnah Brura (seif koton 46) don't seem to apply here, so maybe this is different.