This is how Jeff Tweedy plays this song on Sunken Treasure: Live in the Pacific Northwest
Capo 2

INTRO
G  D   C  G

I'd like to rest my heavy head tonight
       D
On a bed of California stars
              C
I'd like to lay my weary bones tonight
       G
On a bed of California stars

I'd love to feel your hand touching mine
             D
And tell me why I must keep working on
          C
Yes I'd give my life to lay my head tonight 
       G
On a bed of California stars

G  D   C   G

I'd like to dream my troubles all away
       D
On a bed of California stars
C      
Jump up from my star bed make another day
      G
Underneath my California stars

They hang like grapes on vines that shine
              D
And warm a lover's glass like a friendly wine
         C
So I'd give this world to dream a dream with you
        G
On our bed of California stars

G   D    C   G

I'd like to rest my heavy head tonight
       D
On a bed of California stars
              C
I'd like to lay my weary bones tonight
       G
On a bed of California stars

I'd love to feel your hand touching mine
             D
And tell me why I must keep working on
          C
Yes I'd give my life to lay my head tonight 
       G
On a bed of California stars

G  D   C   G

I'd like to dream my troubles all away
       D
On a bed of California stars
C      
Jump up from my star bed make another day
      G
Underneath my California stars

They hang like grapes on vines that shine
              D
And warm a lover's glass like a friendly wine
         C
So I'd give this world to dream a dream with you
        G
On our bed of California stars

G   D     C    G
                       D
Dream a dream with you
        C
So I'd give my life to lay my head to night 
      G
On a bed of California stars.

G     D      C     G