If you have made mistakes at a bank which caused you to be blacklisted by ChexSystem, your only option to open a bank account will likely be a second chance checking account. Kyle at Amateur Asset Allocator has a review of this type of account.
I was going to suggest the Huckabay internet banks
(Redneck Bank, Evantage Bank and AmericaNet Bank) as banks that offer second chance checking accounts. They actually call them You're Approved Checking, and they all have a $5/month maintenance fee with no overdrafts allowed. However, all three banks say they've sold out of these accounts. Evantage and AmericaNet continue to offer their 4% reward checking accounts and their 2% Mega Money Market accounts, so I'm surprised to see these You're Approved Checking Accounts "sold out" when they have no interest and a $5 per month maintenance fee.