Hey guys :)
I watched one of his videos and found out that the chords were very easy!
(This was the video btw: http://www.youtube.com/watch?v=E5WY0w34rOE&feature=related)
I am pretty sure that my chords are right, but please comment if they're not.
So here is it, good luck:

Am: 002210
F: 033210
G: 320033

You actually play the chords throughout the song in the same way.
No capo needed.

Am               F              G          Am
Well my eyes are closed, but my heart's on fire
Because the clock is approaching the midnight hour
I leave my window open, all the lights are out
And from the darkest night comes the lightest shout

Am   F     G         Am
Moonshine, moonshine moon
The cow jumped over the moonshine moon
Moonshine, moonshine moon
I'll love you tonight under the moonshine moon

           Am               F                   G      Am
Well as we walk through the streets, there's no-one nowhere
And our nightgown's trailing and our feet are bare
I don't know where we're going and I don't care
Just as long as you're here and the moon's up there

Am   F     G         Am
Moonshine, moonshine moon
The cow jumped over the moonshine moon
Moonshine, moonshine moon
I'll love you tonight under the moonshine moon

    Am             F               G         Am
Now all the little boys and girls around the town
Dreaming through the darkness 'till the moon goes down
But me and my baby gonna be up all night
Dancing under the moonlight

Am   F     G         Am
Moonshine, moonshine moon
The cow jumped over the moonshine moon
Moonshine, moonshine moon
I'll love you tonight under the moonshine moon