Capo 7! I think these are the correct chords. Improvements are welcome! I had a tough 
time figuring out the chords to the bridge towards the end, perhaps you could figure that out.

Intro: G D Em C

Verse 1:
   G (320003@1)                           DHere (xx0232@1)I am, looking up from a long way down
                  Em (022000@1)                         CDidn't (x32010@1)know I was falling till, my head hit the ground
  G (320003@1)                               DTake (xx0232@1)my hand, you're the part of me I won't hide
                  Em (022000@1)                                  CDidn't (x32010@1)know I was standing still, till the world almost passed me by

Chorus:
          G (320003@1)              DIf (xx0232@1)we let go now, would we fall down?
       Em (022000@1)                                CAre (x32010@1)we holding on too tight for this to be real love?
          G (320003@1)              DIf (xx0232@1)we let go now, would we fall down?
       Em (022000@1)                        CAre (x32010@1)we holding on too tight are we holding on
               G (320003@1)            DFor (xx0232@1)this to be real, real, real
               Em (022000@1)           CFor (x32010@1)this to be real, real, real
               G (320003@1)       DFor (xx0232@1)this to be real, yeah
               Em (022000@1)      CFor (x32010@1)this to be real, yeah

Verse 2:
G (320003@1)                                   DHere (xx0232@1)we stand, in the place where you turned me round
                          EmNot (022000@1)what I thought I'd be fighting for
                        CBut (x32010@1)it's the closest to love I've found, found

Chorus:
          G (320003@1)              DIf (xx0232@1)we let go now, would we fall down?
       Em (022000@1)                                CAre (x32010@1)we holding on too tight for this to be real love?
          G (320003@1)              DIf (xx0232@1)we let go now, would we fall down?
       Em (022000@1)                        CAre (x32010@1)we holding on too tight are we holding on
               G (320003@1)            DFor (xx0232@1)this to be real, real, real
               Em (022000@1)           CFor (x32010@1)this to be real, real, real
               G (320003@1)       DFor (xx0232@1)this to be real, yeah
               Em (022000@1)      CFor (x32010@1)this to be real, yeah

Bridge:
            ?                        ?
I wonder if real love can be found, build me up to pull me down
C (x32010@1)              GHold (320003@1)me close or let me go
        ?                                        ?
In this world we built for us, though it doesn't look like much
C (x32010@1)                   DIt's (xx0232@1)always been enough

Chorus: (* = strum once)
          G*                D*
If we let go now, would we fall down?
       Em*                          CAre (x32010@1)we holding on too tight are we holding on
               G (320003@1)            DFor (xx0232@1)this to be real, real, real
               Em (022000@1)           CFor (x32010@1)this to be real, real, real
               G (320003@1)       DFor (xx0232@1)this to be real, yeah
               Em (022000@1)      CFor (x32010@1)this to be real, yeah

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Thanks!