I have an entry on Chexsystems that is almost five years old. It actually doesn't even belong to me, but rather to my father with whom I share my name. The last four digits of the SSN on the report don't even closely match mine. However, Chexsystems is steadfast in their refusal to remove it.
To that end, I have had to circumvent Chexsystems and open my accounts at banks that do not subscribe to that silly service. In my experience, there are many credit unions that do not pull Chexsystems, including NASA FCU, PSECU, PenFed, Navy Federal, Apple FCU are just a few. I know Dept. of Commerce