Aarthi's comment is, I think, really the best approach. Until there are enough people who naturally hang out in chat, people have to "seed" it by making more of an effort to hang out there and talk about things ... or even to play. (Depending on the game, players may want a separate room. Random comments may work better in some play-by-chat games than others.) And it's not like seeding the main site by asking questions we really aren't facing, because this is simply making people more available in case someone drops by for whatever reason ... quality of conversation in chat isn't at all the same type of issue as quality of questions on the site.
I don't think this is much different than asking how to grow the site in general, because everything basically depends on everything else. Chat becomes more active with more people on the site. More people means more questions, more answers, and more meta activity. More people in chat means more off-topic questions diverted there (because there's actually someone around to answer, or to try to answer; it doesn't sound quite the same to say "you can ask this in chat, though" when no one is there to help) and more conversation. More conversation in chat can lead to more questions on the main site. It's just hard when the site hasn't yet reached critical mass and it isn't clear how we can get more active participants on the site.