I'd guess if you already had an account they'd transfer you to CLI, but mine was a fresh application and it just rang, got the recorded "Your call may be recorded" then a guy answered and I dealt with him the entire time.
I just got my chase card about a month ago and called on activation to get a CLI. I called the credit analyst number and there was NO hard pull to get my CL to go from $1500 to $5000, so my advice would be to at least try if you have some other cards with limits higher than the $500 that you've been responsible with.
Jimmy- A recon (reconsideration) is when you call a backdoor number (a number that gets you to an analyst and not a regular customer service rep) to get what you want. This could include credit line increases (cli) Apr drops, or reconing after you were denied a cc through the company.
7/3/08- EQ= 642 UTIL=98% (12/07) 87%((4/08)-41%(5/08)-29%(06/08) GOAL- >9% by 12/08