I sometimes see the link if I have been doing a lot of comments, but I was wondering if there was a way that I could just suggest a chat room from the beginning.
Other than manually creating one and linking to it, sadly there is not, as much as I also wish that was a feature of the SE system.
If you have 100 reputation on any SE site, you can create chat rooms by going to the site chats page and then clicking Create a New Room. Then go in to the room and copy the url. Note that the other person can only talk in chat if they have at least 20 reputation unless someone grants them write access to the room specifically (which requires them first connecting to chat to get a chat account automatically created).