This isn't correct if you're trying to sing along with the album version, but I've 
been covering this song with these chords for a while now and it sounds great.

Capo 4 (All chords relative to capo)

Intro (repeat 2X): C, G, D, Em (hammer on/off of the "a" string)

Verse I:

C (x32010@1)       G (320003@1)         D (xx0232@1)             Em (022000@1)    CI'm (x32010@1)not sure why it always goes downhill
           G (320003@1)       D (xx0232@1)             Em (022000@1)   
Why broken cisterns never could stay filled
            CI've (x32010@1)spent

Chorus I:

G (320003@1)           D (xx0232@1)     EmTen (022000@1)years singing gravity away
        C (x32010@1)             G (320003@1)             D (xx0232@1)   Em (022000@1)   
But the water keeps on falling from the sky

Verse II:

C (x32010@1)        G (320003@1)              D (xx0232@1)                Em (022000@1)   CSo (x32010@1)here tonight while the stars are blacking out
           G (320003@1)                 D (xx0232@1)         EmWith (022000@1)every hope and dream I've ever had in doubt
             CI've (x32010@1)spent

Chorus II:
     
    G (320003@1)             D (xx0232@1)                 EmTen (022000@1)years trying to sing these doubts away
        C (x32010@1)            G (320003@1)             D (xx0232@1)    
But the water keeps on falling from my eyes
    C (x32010@1)    G (320003@1)    D (xx0232@1)    Em (022000@1)     CAnd (x32010@1)heaven knows, heaven knows
                  G (320003@1)          DI (xx0232@1)tried to find a cure for the pain
C (x32010@1)   G (320003@1)      D (xx0232@1)             Em (022000@1)   C (x32010@1)      
Oh my Lord, to suffer like you do
              G (320003@1)    D (xx0232@1)   CIt (x32010@1)would be a lie to run away

G, D, Em, C

Verse III:

G (320003@1)  D (xx0232@1)                 Em (022000@1)     CSo (x32010@1)blood is fire pulsing through our veins
             G (320003@1)        D (xx0232@1)                  Em (022000@1)
We're either riders, or fools behind the reigns
             CI've (x32010@1)spent

Chorus II

Bridge:
C (x32010@1)           G (320003@1)       DIt (xx0232@1)keeps on falling
             Em (022000@1)     CIt (x32010@1)keeps on falling
            G (320003@1)       DIt (xx0232@1)keeps on falling
            Em (022000@1)   
It keeps on falling
        C (x32010@1)            G (320003@1)             D (xx0232@1)  
And the water keeps on falling from my eyes

Chorus II

Ending:

C (x32010@1)      
              G (320003@1)    D (xx0232@1)   CIt (x32010@1)would be a lie to run away