Most companies have a policy that any work done on premises and on company time are the property of the company. The exceptions to this are typically handled on a case-by-case basis in a contractual agreement.
If this person is valuable, it might be advisable to put out a company policy brief and discuss it with him as one final warning, advising him that from this point on, any work he does within the confines of your company's walls and on company time would be the intellectual property of your company. That might be enough for him to wise up and not work on his own stuff on company time.
If you don't feel it's worth it to keep this person around, then you've already warned him. It may be time for action.