Every Mondays at 7 p.m., the venue is Iguana Café, 517 N. Halsted. I've been there (though not for chess): it's very nice. The restaurant reviewers on UrbanSpoon give it a 92% rating , and the average entrée price is under $10.
For more info, join the meetup group.
Café owners tend to get annoyed with chess players who hang out all evening and only spend $2 for a cup of tea. If too many chess players do this, the owners eventually ask the chess players to leave. If, on the other hand, the players patronize the restaurant, the owners may start looking for ways to bring more chess players in.