I'm quite fond of Chickie's and am happy you enjoyed it too. I especially like their different take on giardiniera, very fresh and bracing. Chickie's is among the better beef stands in Chicago yet not that many people seem to know about it.
The way I understand it, Chickie's 2 on Cermak in Cicero used to be run by the same couple but they found it too much trouble to deal with two places so sold it off not long ago. I stopped in once late last year and found the product (beef--dipped, hot) to be quite a reasonable approximation of the original.
I'm wondering if JR's Caribbean Hut on S Ashland might now be under new management. I'm pretty sure it was closed for several months late last year/early this year. You say it was carry-out. While I'm sure that was most of their business, they used to have several tables in the front area. And I sure don't remember seeing tips and ribs on their menu. On one of the barbecue expeditions about 5 months ago I remember noticing a then-vacant storefront on Indiana (in the 30s I think) that had a big sign in the window stating it was the new home of JR's. I'll post an update if I can find out anything new.
While I thought JR's jerk chicken was pretty good when I last tried it a little over a year ago, I've long been partial to Tropic Island (1922 E 79th). Jerk chicken and house-made ginger beer are the things to get.