I know that the term chattorumu is used for online chats. What term would be used to denote an actual room for this activity? A room to chat in.
Though I'm not sure whether a real chat room has ever existed in English-speaking world (after a bit of Googling), and I'm not sure it's the perfect match for the hypothetical concept, I know that some facilities actually have 談話室【だんわしつ】 for close or private small-group conversation. A number of diners (mostly cafés) seem to have it as a part of the trade name too.
Last but not least, this word is also not uncommon for the name of online chatrooms or forums.