Credit Union That Doesn't Use ChexsystemsThe CIT Bank Savings Connect account is the best among banks that don’t use ChexSystems. Here are 15 credit unions that don’t use ChexSystems. United Heritage Credit Union in headquartered in Austin TX now accepts anyone who join the Texas Consumer Council with a $15 lifetime fee. NFCU offers five unique checking. Out-of-network ATM withdrawal fees may apply with Chime except at MoneyPass ATMs in a 7-Eleven, or