It depends on how strong your culture is, quite frankly. If you've really nailed the culture--connecting what's deeply valued there to what actually drives the success of the enterprise--and this person really doesn't fit, then I'd lean towards helping them find a new job. If they don't value what the system values, it's usually really hard to change that.
On the other hand, it may be an opportunity to look at your culture if you haven't in a while. "Doesn't fit the culture" might be an indicator that the culture is in need of a shift more than that individual.