I like your idea of giving students the option of either attending the Live Chat or completing an additional assignment, Marina! Usually there has to be some type of incentive for students to attend chats, even though one would think that graduate students, in my experience, would have intrinsic motivations to attend chats and improve their understanding of the assignments and the course content.
I have often offered "bonus" material to students who attend the chats or at least listen to the archives. If they bother, then they'll get some extra help that I don't offer through the classroom in general.
