Love this song, but all of the tabs are very different a none seem right. I've combined all of the 
tabs together to form one superior tab! *Laughs maniacally*

Tabbed partially from this amazing video from Marty Schwartz:
https://www.youtube.com/watch?v=l-QDFak62eY

Also, I took this lyric format from user McLovin905, so check out their version of this tab:
http://tabs.ultimate-guitar.com/c/coldplay/a_sky_full_of_stars_ver2_crd.htm

Some of the chords I don't know the technical names for so bear with me

Capo 6

Am7 [X02010]
A7sus4 [X02030]
Fmaj7 [XX3210]
Fmaj7* [XX3230]
C [X32010]
Cadd9 [X32030]
Em* [020010] or [022010]
Em7 [022030]
Em [022000]

Every other chord is optional; the main chords are Am7 Fmaj7 C and Em*
Trying playing with adding the 3rd fret of the G-String (relative to the capo) by using the other
chords

Am7                     Fmaj7                 C                Em*               
         Cause you're a sky, cause you're a sky full of stars

Am7                     Fmaj7                 C                Em* 
       I'm going to give you my heart

Am7                     Fmaj7                 C                Em* 
         Cause you're a sky, cause you're a sky full of stars

Am7                     Fmaj7                 C                Em* 
       And cause you light up the path



Am7            Fmaj7           C                Em* 
       I don't care, go on and tear me apart

Am7            Fmaj7           C                Em* 
       I don't care if you do

Am7            Fmaj7           C                Em* 
    Cause in a sky, cause in a sky full of stars

Am7            Fmaj7           C                Em* 
I think I saw you



Am7 Fmaj7 C Em*  x3



Am7                     Fmaj7                 C                Em*               
         Cause you're a sky, cause you're a sky full of stars

Am7                     Fmaj7                 C                Em*
       I'm wanna die in your arms, oh

Am7                     Fmaj7                 C                Em*
         Cause you get lighter the more it gets dark

Am7                     Fmaj7                 C                Em*
       I wanna give you my heart



Am7            Fmaj7           C                Em*
       I don't care, go on and tear me apart

Am7            Fmaj7           C                Em*
       I don't care if you do

Am7            Fmaj7           C                Em*
    Cause in a sky, cause in a sky full of stars

Am7            Fmaj7           C                Em*
I think I see you

Am7            Fmaj7           C                Em*   
I think I see you



Am7 Fmaj7 C Em* x4

(Strum once each from now on, also play a regular Em)

Am7 Fmaj7 C Em x2



Am7    Fmaj7                 C                   Em
      Because you're a sky, you're a sky full of stars

Am7    Fmaj7                 C                   Em
Such a Heavenly view

Am7    Fmaj7                 C                   Em
Such a Heavenly view

Am7 Fmaj7 C Em x2