The HR department at the company that I am currently working for has requested that I provide a system for storing employee social security numbers in our company database. The
My recomendation: store your MySQL data on encrypted disks, so that in the event of laptop misplacement, etc, the data cannot be retrieved.
If the database application itself is compromised, of course, nothing can help, as the application itself uses the SSNs. Perhaps that is a design flaw you can correct. I would tend to think in terms of a small, limited application that maps SSN to a (non-SSN) key, and then using that new key as the "user ID" in your database rather than the SSN. I would avoid proliferation of the SSN itself at all costs.