I'm quite lucky in so much as I can generally "hear" certain chords (in fact I kind of see it rather than hear it, but that's another thread) and can usually work a song out for myself. I'm slow with written music and tend to rely on my ears unless I'm playing something particularly tricky.
That said, I wouldn't hesitate to ask for chords to a melody I already know if I thought I was missing something.
Just knowing the melody isn't enough. You can completely change the feel of a song with some slight chord alterations.
C-flat.