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Nice!
Nothing wrong with $500 starting CL. Use it and build your relationship with Chase. Only good things will happen creditwise.
Congrats on getting the card! It's a good one. As for the auto CLI, it seems to be a ymmv situation. Lately, it seems quite a few people have received unexpected increases. Sorry to say, I am not one of them.
Auto CLI's with Chase are random at best. Down the line when your overall credit picture has improved you can bite a hard for an bigger increase.
OP, call back and talk with someone else tomorrow. There have been many people, including myself, who called in for more than one recon. If I would have taken what the first agent I talked to as gospel, I would have never called back again and wouldn't have gotten my card. Basically I was declined and the 1st rep told me to wait for 2 years until my current accounts aged a bit. I had a few drinks, got my liquid courage up, and called back about 4 or 5 hours later and got another representative that approved me with a $5K limit.
Ummm all of this just happened yesterday so I encourage you to call back and plead your case to as many agents as you can until you get what you want. Just remember their names and voices in case you get the same person again....LOL!