I use the chat regularly. There are lots of interesting intellectual discussions, and it is a real time forum for networking. It is no more or less valuable than the forums, which produce 90% garbage and 10% valuable activity. Like most of what people say in any medium, it is 90% garbage 10% useful. If you close the chat you might as well close the forums too.
And since the internet is one giant consanguineous interchange of the same information, consisting mostly of links, you might as well limit your site to original content if you get rid of the chat and/or the forums.
Paying people to delete most of the user generated content and to preserve mostly reposted links is probably a waste of money if you're worried about serious criminal liabilities.
However, if you want to provide an open forum for discussion the chat is a valuable part of that. On the other hand, if the site mainly exists to generate a profit, then the 100 or so users who use it over any given 3 month period probably do not cover the cost of maintaining it in donations.