From what I can tell, the chords seem to repeat pretty much throughout the whole song.  
These chords work on piano, but I'm not particularly good at guitar (I'm still teaching myself).

The chords are Am, C, G, Am.


Am        C           G          Am                   Am
There's a game in the world, a little bit of cat and mouse
         C             G         Am
With the boys and the girls, and if I had to ante up
Am  C          G             Am                            Am
I'd bet on the birds, 'cause they don't have to get caught up
         C             G            Am                     G
With the boys and the girls and a little game of cat and... mouse


CHORUS

Am (x4)        Am (x4)
Mommy did it, daddy did it
Am (x4)       G (x4)        Am (x4)
Funny little monkeys in the zoo will do it
Am (x4)         Am (x4)
Stupid does it, ugly do it
Am(x4)    G (x4)       Am (x4)
Only the unlucky of us get to do it

Am    C              G         Am
.... .... Let's fall in love...
Am    C              G         Am
.... .... Let's fall in love...


(The rest should be the same, except I'm not 100% sure if the instrumental break is the same...)

There's a game in the world, a little bit of cat and mouse
With the boys and the girls, and if I had to ante up
I'd bet on the birds, 'cause they don't have to walk around
With the boys and the girls and a little bit of cat and mouse

Mommy did it, daddy did it
Even though I bet they wish they really didn't
Mary did it, Joey did it
Even little baby baby Jesus did it

Yuppies do it, junkies do it
The funny little monkeys in the zoo will do it
The stupid does it, the foolish do it
Only the unlucky of us get to do it

Let's fall in love
Let's fall in love

Mommy did it, daddy did it
The funny little monkeys in the zoo will do it
The stupid does it, the ugly do it
Only the unlucky of us get to do it

来源：www.ultimate-guitar.com