Access to subfolder without having access to parent folder

Greetings!
I need for a user to be able to access a subfolder by browsing through the directories, but I don’t want the user to be able to see any files in any of the folders above this folder.
Does anyone know how to accomplish this?
I have given the user the traverse folder permission, but that doesn’t work.
They seem to only be able to browse through the folders if I give them read rights on the folders. This however, allows them to see the files in the folders.

Any ideas are greatly appreciated.

Thank.

Chad London