Alright, this song is divided in three parts. 
The first part is almost completely piano, 
the second is almost completely strings and other ambience,  
and the third part is almost completely guitar.  
Also, Coldplay tunes their guitar's 1st string to D and capos it on the 7th fret.  
If you want to go ahead and figure out the chords, be my guest.  
It sounds like 4/4 but it's actually 6/8, 
which was confusing for a while.  
Just count the song and you'll see.

(1st part, just strum once to simulate piano)
               DThe (xx0232@1)birds they sang, at break of day.
       G/BStart (143121@7)again, I hear them say.
        C#dimIt's (3423xx@1)so hard to just walk away.
               DThe (xx0232@1)birds they sang, all a choir.
       G/BStart (143121@7)again, a little higher.
       C#dimIt's (3423xx@1)a spark in a sea of grey

(2nd part, again strum once)
    Em9 (022032@1)  GThe (320003@1)sky is blue.
           Em9 (022032@1)          GDream (320003@1)that lie, 'til it's true.
     Asus4 (x02230@1)A (x02220@1)      Asus4 (x02230@1) AThen (x02220@1)taking back the punch I threw.
   Em9 (022032@1)     GMy (320003@1)arms turn wings.
         Em9 (022032@1)  GOh (320003@1)those clumsy things.
        A7 (x02020@1)                 Gmaj7Send (xx5432@1)me up to that wonderful world.
    Em7      A7 (x02020@1)        DAnd (xx0232@1)then I'm up with the birds.

(Sort of bridge thing)G  Gadd(#4)  D

(3rd part intro, one chord per measure)
D Dsus4 D Dsus4 D Dsus4 D Dsus4

(3rd part)
               D (xx0232@1)           Bm (x24432@1)         D (xx0232@1)   BmMight (x24432@1)have to go where they don't know my name.
           Gmaj7 (xx5432@1)  G6 (320000@1)          Gmaj7 (xx5432@1)      G6Float (320000@1)all over the world, just to see her again.
       D (xx0232@1)           Bm (x24432@1)     D (xx0232@1)    BmBut (x24432@1)I won't show or feel any pain.
      Gmaj7 (xx5432@1)       G6 (320000@1)          Gmaj7 (xx5432@1)      G6Even (320000@1)though all my armo(u)r might rust in the rain.
          Em7
A simple plot, but I know one day,
      G (320003@1)                   D (xx0232@1)    Bm7good (x20202@1)things are coming our way.
          Em7
A simple plot, but I know one day,
      G (320003@1)                   D (xx0232@1)    Bm7good (x20202@1)things are coming our way.
   G (320003@1) D/F# (200232@1)name="chord_320003@1">G   A (x02220@1)name="chord_320003@1">G   D/F# (200232@1)name="chord_320003@1">G   A (x02220@1) 
Oh yyyyyyyeeeeeeeeaaaaaaaaaaahhhhhhhhh!

(outro, again, one chord per measure)

D Dsus2 D Dsus2 D Dsus2 D Dsus2 D6