No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
As odd as it sounds, it seems that Chase would give preference to a credit profile that is thick, over one that is thin, even when comparing a thick profile with mediocre (or bad, even) payment history to a thin profile with perfect payment history.
My payment history is fairly bad (even with past Chase cards that have been charged off), but my file is pretty thick, with lots of cards over the years that had great histories and high limits (mixed in with a few others that had bad histories). Chase disregarded my crummy payment histories in my reports, presumably because they had a LOT of revolving account data to work with. They saw that, even with bad past experiences with me, it appeared like I was on the right track again, and approved me for a couple new cards with good limits. Without a lengthy and thick credit file, it would be hard for them to make that determination.
A single $1,000 credit card isn't enough information for them to work with. Pretty much anyone can handle a $1k card, even if it's maxed out it's only like $25/month to keep your payments current. But a $10k or $25k card is a totally different animal - it could quickly become unaffordable to stay current on payments with a card of that SL. So Chase wants to see how you're able to handle high SL cards before they want to give you one themselves. Again, as odd as it sounds, they'd rather see someone who has experience with them (even bad experience) than someone who has no experience with them. I know it makes no sense, but it's what their Profit and Loss calculators came up with for some reason.