After being denied a CLI via the "secure message" feature on the website, I contacted the backdoor number for Chase Credit Analyst that I found on this board.
After two or three minutes of silent hold, a very polite and helpful rep came on. I explained that I had been denied for a CLI and wanted to request reconsideration. He put me on hold while he reviewed my file, then came back and went over it with me. He pointed out two accounts that I had lates on from 2007, a student loan and a car loan, and said that was why the system had denied me. I explained to him that the student loan was in forbearance, and that I had gone all the way to the ombudsman to have it corrected, with no success, and mentioned the difficulty of large bureaucracies. I told him that the lates on the car loan were legitimate, and that it was due to a change in employment. I also pointed out that I had since paid off both loans in full and had a great history with Chase. He agreed, and pointed out that although I used the card a lot, I always pay in full each month. He appeared to see both of those as positive traits.
He said that he would process the reconsideration for me, and asked me a several questions including length of employment, why I wanted an increase, etc. He also asked me what limit I wanted. I told him I'd like to be in the 15k to 20k range. I explained that I used the card for reimbursable business expenses but sometimes got too close to the limit for my own comfort and ended up using another card. I also explained that I tried to keep my utilization low in order to make sure my credit report was not adversely affected.
After a brief hold, he returned and offered me an increase to 10k, which I accepted.
The key take-away from this: The last small paid collection from Verizon is not hurting me. The lates, even though they are old, are still flagging me for an automatic no in the Chase computer.
