He uses a fingerpicking pattern throughout most of the song.
For the C chord it would be this:

------------------ | ------------------ | 
-0-----0-----1---- | -0-----0-----1---- | 
------------------ | ------------------ | 
---3-----3-------- | ---3-----3-------- | 
------------------ | ------------------ | 
------------------ | ------------------ | 


C             F2             C
I am sweating bullets in the shade.

C             F2             C                       F
I am drinking whiskey on the morning of your wedding day.

            Am   Am/G  C   F2   C
I think I'm weightless now.

             G         Am         G             C
So I'm gonna sing hallelujah, the ship is goin' down.

C                 F2                C
Amy's friends all think I'm full of s---.

    C                F2            C                     F
But all those m----- f-----, don't even know the half of it.

              G         C
They've never felt that cold.

             G           Am              G                C
So I'm gonna walk to the west coast, the South is getting old.


C     F     Am     G     Am     G     C


C                F2            C
Lately I've been lookin' for a fight.

  C                 F2
I haven't felt this anxious since the

C                 F             G      C    F2       C
day that I was baptised back in ninety-five.

             G                 F
So I'm gonna greet them with a smile.

Am                F
Talk sports for a while.

G              Am          G             C     C/G     C     C/G
Knock a couple back on the front porch tonight.