With 20 reputation you gains the chat privilege, as described here, but I couldn't find this option in a user profile.
Where should I look for it?
You won't find the chat links in user profiles, it is located in the top right on the black bar, in the little stack exchange hamburger "community" menu, it can be a bit hard to find.
It is also located on the footer of every page
Here is a direct link too, just for completeness