While working on a project for my company, I needed to build functionality that allows users to import/export data to/from our competitor's site. While doing this, I discovered a very serious security exploit that could, in short, perform any script on the competitor's website.

My natural feeling is to report the issue to them in the spirit of good-will. Exploiting the issue to gain advantage crossed my mind, but I don't want to go down that path. 

So my question is, would you report a serious vulnerability to your direct competition, in order to help them? Or would you keep your mouth shut? Is there a better way of going about this, perhaps to gain at least some advantage from the fact that I'm helping them by reporting the issue? 

Update (Clarification):

Thanks for all your feedback so far, I appreciate it. Would your answers change if I were to add that the competition in question is a behemoth in the market (hundreds of employees in several continents), and my company only started a few weeks ago (three employees)? It goes without saying, they most definitely will not remember us, and if anything, only realize that their site needs work (which is why we entered this market in the first place). 

This might be one of those moral vs. business toss-ups, but I appreciate all the advice.

Though I'd love to live in a world where it would be perfectly safe to just drop them a note to let them know, I'd suggest involving your legal department first.  Realistically, it's entirely possible that however well intentioned your bug report is, someone in the competitor's organization will interpret it as "our competitor just paid one of their employees to hack our site".  That perception could create legal or PR issues for both you and your company.  Involving your legal department in the notification should help shield everyone from the appearance of impropriety.  Of course, that creates the possibility that the legal department concludes that notifying the competitor creates an unacceptable legal risk and tells you just to sit on the information.  But that's much better than  the alternative that it all blows up in your face.