Initial approval was $1000. Current limit is $6000. I believe I've had the card about a year. Got one auto-CLI after about 3 months (to $2500 IIRC) and then after another four months to $6000. It's probably time for me to ask for another.
Finally got around to calling in for the CLI. Only asked for another $1500 and got it. New CL is $7500. That makes this card once again my highest CL, and should give AMEX and Chase something to shoot for on the next round of CLI's.