For those who don't know, credit card checks are blank checks that your credit card company sends you. When you fill them out and spend them, you are taking a cash advance on your credit card account. You should be aware that taking a cash advance on your credit card normally has extra fees and finance charges above what you have with regular credit card transactions.
That having been said, when you take one of these to your bank and try to deposit them, it is entirely up to bank policy how long they will make you wait to use these funds. They want to be sure that it is a legitimate check and that it will be honored. If your teller doesn't know the answer to that question, you'll need to find someone at the bank who does. If you don't like the answer they give you, you'll need to find another bank.
I would think that if the credit card is from Chase, and you are trying to deposit a credit card check into a Chase checking account, they should be able to do that instantly. However, bank policy doesn't always make sense.