I requested a new card through the customer portal last week, as the chip on my CSP had stopped working. The replacement arrived today in the mail, and the letter that accompanied the card noted a Credit Access Line of $9,000, up from the $5,000 starting limit that I was approved for back in November.
I've only had the card for four months, and haven't used it a whole lot lately in an effort to meet minimum spend on my Citi AA Platinum ($5,000 SL), but Chase almost doubled my limit. I know Chase is known for being less than generous with CLIs, but there's definitely hope!
For reference, I'm 19 and a full-time college student. I've been an AU on my mother's American Express Green card (no pre-set limit) for a little over a year. I have a Chase Freedom ($4,500 SL), as well. My FICO score is in the mid-700s, and no derrogatory items.