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.
MidWest America Federal Credit Union
They use a system available through TeleCheck.
They do not use ChexSystems or any kind of credit check at all. To open an account just bring 2 forms of ID.
Members Source Credit Union
They do not use ChexSystems or a credit report.