This question has been closed on the grounds that it is a "duplicate" that "already has an answer". However the indicated duplicate is another post from two years ago, has no accepted answer, and the single solution it received is a convoluted process that is effective only for diamond-level moderators. I am not one of those, and few people are.
This issue has been hanging around for far too long without an explanation or a resolution. Accordingly this question should be reopened.
I have been helping a rep 13 user at length in the comments section, and got the automatic prompt to take the discussion to a chat room. Of course I was unable to do this.
The way it seems to me that it should work is that someone of sufficient reputation can invite anyone to a chat room. If not, then please can we silence the prompt telling me to do it!
A similar question has been asked before, but that was a why is it this way rather than a can we fix it like this.
Searching a little more carefully, it seems that this has been raised before here, and here. The gist of the explanation is that the chat server is separate from the main servers, and in the general case it requires an HTTP request to determine a user's chat reputation.
However, this was raised in July 2011 and the questions gained 58 and 82 upvotes respectively. It seems that this feature is highly desirable and I am surprised there has been no movement in 28 months.