This article at DoC on the 5/24 is extensive and fairly recent. It says the following:
Do store cards count towards the limit?
If the card can be used outside of a specific store (e.g it has a payment network such as Visa, Mastercard, American Express or Discover) it will be counted. If it can only be used for a specific store, it will not be counted. Data points: 1, 2
That seems to imply that your card would NOT be counted by Chase toward its 5/24 rule.
Normally I"d say yes. For example, I remember a few weeks ago someone posted asking whether Chase woould permit him to open a bank account while he was visiting NYC. (He resides in a state with no Chase branches.) I remember saying "Why don't you ask them?"
But here we are talking about complex details of a rule that many Chase reps still don't even know exists. I was opening a Chase checking accounf a year ago and the rep was urging me to apply for a Chase card. I told him I'd normally be happy to but I was in violation of the 5/24 rule. He told me that my 830 credit score was plenty high enough and I was sure to be approved. I explained again what the 5/24 rule was and told him I didn't want to burn an inquiry when I was sure to be turned down. He still assured me I'd be approved -- 100% certainty. Naturally, I was rejected and an inquiry was burned anyway.
The point of that story is that he and his bank manager had no idea about the 5/24 rule. So if people fairly high up on the chain don't even know the rule exists, it strikes me as inlikely that you'll get an accurate answer about a very abstruse detail within the rule.
Is your FICO score and income high enough that you should definitely be approved for the Chase card you are considering -- assuming that 5/24 does not apply to you? If so, I think you should step up to the plate and take a swing for the sake of science. Apply for the card and let us know whether you get approved. But note that it only proves something if your score and income are otherwise very sound. So if your application is otherwise borderline I would not apply.
Darn. Another datapoint lost to science due to consumer cowardice!
Just joking with you pal. Always important to do what you think is right. If you do go the route of being removed as an AU, make sure that the "removal" gets completed reflected in all three credit reports before you apply. That AU record needs to be completely expunged -- otherwise it will show that you had an AU card added in the last 24 months. The 5/24 rule doesn't care about whether you later close cards, just when they were opened.
The creditor will say "yes" in all likelihood. But you still need to check your credit reports yourself and make sure that the account is completely gone. It may just end up reading as "closed." In which case you may have additional work to do with the credit bureau to get it removed. If that happens there will be people here on the forum who can advise you on how to get it completely deleted.