FM Chat works great in FileMaker Go and we've provided a Go-specific interface file called "FMChat Go.fmp12" optimized for FileMaker Go on iPad.
Host that file along side "FMChat.fmp12" and ask your Go users to open the Go version instead of the regular FM Chat file. The two files share the same data.
There are just a few behavior differences when using FM Chat in Go:
Despite the template or theme set in your user profile, chats in Go are always displayed in a special FM Go theme that looks like a simplified version of "iChat".
User avatars don't show up inside the chat on Go, but you'll still see the user's avatar in the Members pane and see their name ("Jane said:") inside the chat.
Growl notifications don't work in Go.
When attaching files to a chat, you only have access to those files in FileMaker Go's "Files on Device" list (including "Other Documents")