I would start with Chase but call them, not write them a letter. I'm impressed with a recon they did for me recently over the phone. The backdoor number I used was 888-245-0625. I don't know your exact situation but maybe something like "I've heard a lot of good things about...(insert whatever card you applied for here) and about your company".
Also be honest and pleasant. I think that will go a long way with people if you are nice. If asked why you have so many inquiries, be ready to have a good answer. It sounds like you are trying to establish some good credit history, which can be difficult when you don't have any. Tell the analyst that and hope they are sympathetic.
Good luck. Keep us updated on how it goes.
