Yes BackupChain has the option to back up and restore file and folder permissions, so-called ACLs.
You’ll find the backup option in the Options tab, box “Access Control Lists”.
When restoring, at the very end of the restore screen where you enter the target folder, click ‘advanced options’.
You’ll see an option there to restore ACLs on folders and files. Check both and proceed.
Note that you need to use NTFS formatted target folders in order to preserve ACL information.