This song is very simple, and very beautiful. Here are the underlying chords!
Barre chords sound better for this, and they're slightly easier, but non-barre works as well.


B
Blue
A
Sky
G#m
Sun
G
Shine
B
Be
A
Mine
G#m
Star
G
Eyes


G               F#
I can't catch it
E               F#
I can't catch it
E
I can't catch it


B
Love
A
Please
G#m
Come
G
Back
B
Send
A
You
G#m
Cry
G
Gone


G              F#
I can't catch it
E              F#
I can't catch it
E
I can't catch it


B
Please
A
Please
G#m
Sun
G
Shine
B
Be
A
Mine
G#m
Come
G
Back


G              F#
I can't catch it
E              F#
I can't catch it
E              F#
I can't catch it
E              F#
I can't catch it
E
I can't catch it


B
Come
A
Back
G#m
Send
G
Love
B
Gone




And there's the chords. Also, just for the heck of it, here's the tab for the high 
guitar part in the very beginning:
e|-------11----------11----------11----------11----------11----------11----|
B|----12----12----12----12----12----12----12----12----12----12----12----12-|
G|-11----------11----------14----------14----------13----------13----------|
D|-------------------------------------------------------------------------|
A|-------------------------------------------------------------------------|
E|-------------------------------------------------------------------------|

e|-------11----------11----|
B|----12----12----12----12-|
G|-12----------12----------|   Repeat forever
D|-------------------------|
A|-------------------------|
E|-------------------------|