Banks that do not use ChexSystems
Somewhere between 10 and 20 percent of banks are non ChexSystems banks. That number is dwindling rapidly, and more sign up each day. In many cases, you might not even be able to find banks not using ChexSystems in your town. However, you don't have to stop there. There is no law that says you cannot use an out of town, or even out of state bank (or even an out of the country one, for that matter). You may well be able to locate a place where you can get a non ChexSystems checking account in another town.
This does however, bring up the inconvenience of banking, since it takes away your ability to drop down to your local branch and make deposits. And yes, it is an inconvenience, but not as big as inconvenience of not having an account at all. Most banks now have at least minimal Internet banking and online bill paying facilities. Direct depositing your paychecks will also eliminate a lot of the headache of depositing your checks, and as a last resort, snail mail deposits are always an option.
Next, consider paper checks. Do you really need them? Some of the non ChexSystems banks are willing to give you a bank account where you can direct deposit your paychecks, give you a debit card to use, and online bill paying facilities. You may not even really need paper checks, and in the end, in today's era of electronic transactions, they are rapidly becoming obsolete. You can do without them.
Do take time to evaluate which banks do not use ChexSystems. You may come up with several options, but take the time to compare the fees. The fees are likely to be a bit higher than your "friendly neighborhood bank", but then again, your local friendly banker doesn't want you. That said, the fees vary a great deal, and there are some non ChexSystems banks that have excellent fee structures. Pay careful attention to things like high "account set-up fees," per-check charges, usage fees for your debit card, etc. Read the fine print and find the best deal.