As the link in quid's answer explains, you can create a new room for you or another user. I will add that it is also possible to invite a user to already existing room.
You first need to find this users chat profile either by searching among users or simply by clicking on they username in chat.1
Notice that then you can see two options there:
- "Invite this user to" with a list of rooms you're currently in. (So do not forget that if you want to invite a user to an already existing you room, you have to be already in this room.
- Start a new room with this user.
1I'll add here that not every user has also a chat profile. Users who never talking chat - and never had comments moved to chat - most likely do not have a chat profile and cannot be contacted in this way. (Moreover, a user has the same username as the parent user. Since some users have different usernames on different sites, it is possible that you might have to try several usernames before you find the right one. However, the users with different usernames on different sites are rather rare, as far as I can tell.)
After these general comments, addressing the question in the title, I will add a few more remarks:
- If you have already started a discussion with a specific user in some chatroom (which is the situation described in your post), then you do not need to invite the user to the chatroom. You can simply ping the user in that chatroom either by using
@username syntax or by using reply function. (Some more details can be found, for example, here: Does ping work in chat with no autocompletion? or Does a direct reply to a message in chat create a notification, no matter what age the message is?)
- If have created a chatroom with the intention to continue discussion you started with some other user in comments - or if you want to use some existing room for this - the reasonable approach is simply to ping the user in comments and include a link to the chatroom. It is possible that some other users who read your discussion in comment might be interested in the same topic, including link to the chatroom provides those users with a link to the place where the discussion continued.