It depends upon the IRC chat client you use. But that said, I've yet to find an IRC client that DOESN'T have a logging option. Usually it's in the form of either text file and/or HTML. (I use the most popular IRC client, mIRC, which does text files, though I think newer releases may allow options for other formats.) Sometimes you have to manually enable logging depending upon the program, but it's usually as easy as clicking a checkbox.