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I am on chexsystems but i know a lot of people who also are and were able to become members of Alliant. It also says on their website that if you are on chexsystems your check card daily limit will be lower.
I filled an online application and went thru security questions, then it said processing for about a minute or so and it asked me if i needed a card and if i needed checks etc... anyways i answered and at the end it said "we will contact you we might need additional information from you". What does that mean?
When I signed up for ACU, I recall it took a couple of days to get everything processed. You could call them in a day or two if you don't hear anything further.
If you're in Chex, you might want to wait a bit before getting cranked up with the new account.