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 or TeleCheck. Most people are still being approved.
They do not use ChexSystems and only use Equifax to check identity. This does not run a full credit report.
First National Bank of Picayune
They use TeleCheck.
Woodforest National Bank
You must apply in person and they are friendly to those reported to ChexSystems.