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I had a 900.00 balance writen off by Citi and sent to collections in 2014--since been PFD with Portfolio. I know my scores aren't ready yet, (598 to 617 depending on CRA) but after continuing to groom them for a while longer I would like their Double Cash card. So the question becomes, "How long is Citi's memory?"..
http://ficoforums.myfico.com/t5/Credit-Cards/Does-Citi-blacklist/td-p/4410620
http://ficoforums.myfico.com/t5/Credit-Card-Applications/Citi-Blacklist/td-p/4394673
Basic answer: "wait it out" -- 7 to 10 years probably.
Come on now, using the search bar is cheating!
It's long, but they are more receptive if you pay it off