I posted this as a comment under @Bill's answer a few minutes ago, but I guess it deserves to be expanded into its own answer since the question is a feature request.
Welcome to Meta Stack Overflow, Tony! I disagree with your feature request, though I wouldn't oppose it if it were to be implemented. There's no way you would have known this coming in, but the chat here is a Third Place, and merely supplements the primary purpose of the site, which is providing expert Q&A (except on Meta; more on that later). That's relevant because I don't think we expect or want new users to enter the site through chat, in general. They're supposed to associate the site with expert Q&A, and only reach chat after using the actual site for a while.
Also, I see that you were trying to participate in Meta Stack Overflow's chat, not Server Fault's or Super User's. It is a chat about Meta Stack Overflow, which is itself a site about how Stack Overflow/Stack Exchange works. Since you have no Stack Exchange experience, you would doubly have no reason to be in the MSO chatroom, except that someone in the chat invited you. This is more understandable right now, since not all sites have had their chats implemented yet, and the MSO chat is still sort of serving as an omnibus chat, but it will become less and less understandable in the future as the sites mature.
Please don't take this personally, I'm not trying to be mean to you personally or to discourage you from participating in general — in fact, I'm always happy to welcome someone else who makes a reasonable post on Meta, like you have — my point is that your use case is non-standard, and not one that we want to encourage.