There's this chord of which name I dunno since I saw a guy playing these chords on 
a youtube video. This is not exactly exactly what he played but I think it's quite better.

Anyway the unknown chord is marked as Cmaj7, but it's actually played like this:

 e|------|------|---3--|-------|
 h|------|------|------|-------|
 g|------|------|------|-------|
 d|------|---1--|------|-------|
 a|------|------|---2--|-------|
 E|------|------|------|-------|



Am 
I see her smile in her sleep
G
I know that she's a dreamer.
Am                      G
Oh, I'll follow every move she makes.
Am                      G
It's been a long, long night.
            Am               G
Say you're mine. Say you're mine.
                   Am
Can I keep you tonight?
G
Tonight... 



Am                                    G
And we dance around just like constellations.
    Cmaj7           F
You keep my body warm.
Am                                   G
And we dance around just like constellations.
         Cmaj7               
You're keeping me awake at night.
      F               Am
You make my body warm.



       Am                Cmaj7         G
And I fall for her like snow from the sky.
Am                        G
Gracefully I land in her arms.
       Am                Cmaj7         G
But I melted away like snow into the ground.
                 Am 
I told her I've gotta go.
      G
I've gotta go.


Am                                    G
And we dance around just like constellations.
    Cmaj7           F
You keep my body warm.
Am                                   G
And we dance around just like constellations.
         Cmaj7               
You're keeping me awake at night.
      F               Am
You make my body warm.


Am                      G
It's been a long, long night
                 Am
You said you're mine.
                    G         Am
I felt so bad but I had to go.
                    G                     Am
No she never wanted me to leave her behind.
                    G               Am
No she never wanted me to leave her.
                               G
(To leave her) So long, so long. 

(Chorus)