Here's what the Diccionario panhispánico de dudas says about chat:
chat. Voz tomada del inglés chat (‘charla’), que significa ‘conversación
entre personas conectadas a Internet, mediante el intercambio de
mensajes electrónicos’ y, más frecuentemente, ‘servicio que permite
mantener este tipo de conversación’. Es voz masculina y su plural es
chats (→ plural, 1h): «Los españoles se conectan a los chats una media
de 6,3 días al mes» (Teknokultura [P. Rico] 8.01). Es anglicismo
asentado y admisible, aunque se han propuesto sustitutos como
cibercharla o ciberplática (→ ciber-). Está igualmente asentado el uso
del verbo derivado chatear, ‘mantener una conversación mediante el
intercambio de mensajes electrónicos’.
So the word chat is not only established but also accepted in Spanish (even though it has no entry in the DRAE) and it can be safely used.
To answer this question, the most common term to refer to a chat room would be
el chat o también sala de chat.
and this can be verified by the number of Google hits. Of course, other expressions such as
sala de charla o sala de conversación
are also valid, but el chat o sala de chat would certainly be the most common terms for "chat room".
Just as a note: until I searched the DPD for chat and found the above quoted entry (a total surprise to me, I must confess), I firmly believed that the word chat shouldn't be used in Spanish; now, my opinion obviously has changed. It's amazing how, thanks to questions like this one, I can learn new facts about my language everyday.