Pretty song, easy to play.
There's some sort of phaser going on, but it sounds nice acoustically, too.
Intro:
(you can throw in quick 9th notes in here and there on the C's for variety...same goes for the verses)
|C|C|C|C|C|Cmaj7|Gm|F|

   C              Cmaj7         Gm        F
By starlight I'll kiss you and promise to be your one and 
C     Cmaj7 Gm F
only.
     C             Cmaj7     Gm           F
I'll make you feel happy and leave you to be lost in 
C     Cmaj7 Gm F
mine.
C                Cmaj7 Gm             F (Emphasised downstrokes on Gm and F)
And where will we go,    what will we do?
Dm        G
Soon said I, will 
C     Cmaj7        Gm                F
know.          And are you just like me?
C          Cmaj7      Gm                F   Dm (Emphasised; cut the
Dead eyes, dead eyes, are you just like me?     F short to make room)
C         Cmaj7           Gm            F
Her eyes, her eyes were as vacant as the seas.
C          Cmaj7      Gm                F
Dead eyes, dead eyes, are you just like me?  And
Dm   G        C                F
all along, we knew we'd carry on
Dm        G      C Cmaj7 Gm F
Just to belong.
   C           Cmaj7        Gm          F
By starlight I know you, as lovely as a wish granted
C      Cmaj7 Gm F
true.
   C             Cmaj7     Gm              F
My life has been empty, my life has been untrue.
Dm           G            C            F
And does she really know, who I really am?
Dm           G (Hold, maybe give it a slow upstroke or something)
And does she really know me?
   C    Cmaj7   Gm                F
At last.....and are you just like me?
C          Cmaj7      Gm                F    Dm (As above)
Dead eyes, dead eyes, are you just like me?
C         Cmaj7            Gm            F
Her eyes, her eyes were as vacant as the seas.
C          Cmaj7      Gm                F
Dead eyes, dead eyes, are you just like me?
C  Cmaj7  Gm                F
Oooohhh...are you just like me?
(Fade and repeat.  The words vary a bit, there's a lot of "ooohhs", etc...)