In addition to the lighting at home, Chanuka candles are lit in shul to publicize the miracle, with the brachot (O"C 671:7).
Which minyanim do this? All maariv minyanim in the shul(*)? Just a shkiya mincha/maariv? Just the earliest maariv in the shul? Just the "main" maariv, whichever one that is?
Does a plag mincha/maariv minyan light? (Most relevant in the southern hemisphere.)
(*) I'm assuming here that they all take place during a time when you can light candles. A 3AM maariv would be excluded in most places, but I've never seen one.