Can you get a virus like the MyDOOM virus by just chatting in chat rooms?

if you're using an irc client, like mirc
or icq, yahoo messenger, msn messenger, or other instant or irc chat apps , yes.
if you click on any link presented to you
even if it is from someone you know, or accept a dcc file transfer on irc. this is usually how these are spread. mydoom is spread mainly by e-mail.
http://www.sarc.com/avcenter/venc/data/w32.mydoom.a@mm.html
but there are many other viruses and trojans etc. spread in chatrooms
such as mybuddy pic, click here to see my picture etc.

I you use IRC the set your client to NOT autoaccept files. most of the onjoin links i have recieved on joining channel are links to virus/trojan downloads (I Once had a persons ISP pull his account because of this). Be VERY wary of files with extemsions like .PIF , .EXE, .SHS, .VBS and others (this is not an exhustive list). you will also see files such as tunes.vbs set your client to automatically block all of these. You will also see such files like nfor example pic.jpg.shs (more than one file extension NEVER accept these). If you go into a channel and someone tries to send these sorts of files to you then tell a channel op if the channel is registered Those with @ in front of their nicknames.

HTH

Woof