"To have a bit of a chat" means to chat (talk) for a little while. So they're saying, "Would you rather take a nap or talk with us?" "Chat" implies that it's going to be a light, fun conversation, not a serious talk.

I'm a native English speaker from the US. This is not a phrase that I am familiar with. It sounds like they are asking if you would like to take a nap or sit and talk (chat). It could be that this is a British expression that I have not heard here in the US. :)