The following banks and credit unions offer excellent features and benefits. While we recommend them, they are not our top picks for the simple reason that they are not guaranteed banks. They have however helped a lot of people, and may be able to help you too.
They do not use ChexSystems and they do not run a credit report at all.
Woodforest National Bank
You must apply in person and they are friendly to those reported to ChexSystems.
Greenbelt Federal Credit Union
They use TeleCheck when opening a checking account.