I disagree with the chorus of "Fire him now!" in the other comments; startups hire a lot of folks straight out of college, so there's a significant chance that the employee in question has never been informed of what is, and is not, appropriate when they want to pursue a romance with someone from the office. What may be acceptable in a college classroom is very different from what is acceptable in an office.
Mistakes happen, words and body language which were not included in the chat log may have been misconstrued... you have one side of the story right now. Get both sides, and give the opportunity for the man to learn.
Involving a lawyer to ensure that you're on the right side of the law is, of course, a damned good idea. Especially if you end up deciding that you want to go down the road of firing.