hi, I have been trying to grasp the chords they're playing on this one -
even though they may play different variations of the chords as seen in the video, 
these go with the song very well

chords used:

     E A D G B e
Bm*  x 2 4 4 3 x
*    x x x x 3 2 very short
Em   0 2 2 0 0 0
**   x 2 0 x x x very short
A    x 0 2 2 2 0
***  x x x 2 2 2 very short
Bmi  7 9 9 7 7 7
Am7  x 0 2 0 1 0
Em/G 3 2 2 0 0 0
G    3 2 0 0 3 3
F#m  2 4 2 2 2 2

you can either play the opening part as chords (Bm D - Em G - A F#m7 - Bm)
or you can, like myself rather strum out individual strings to substitute
for whole chords (thus skipping transitions to D, G and F#m7) - these ar
noted below as *, ** and *** - the good thing about playing it this way is
that you can pretty much leave the fingers of your left hand (for 
right-handed players) in the position of the preceding chord - this makes
for a more consistent sound of the song, I feel. try it out both ways and you'll see.
Please note that I'm using Bm and Bm* which is the same chord only played 
at different parts of the neck.

Bm*           *    Em         **   A          ***     Bm*

Bm*           *    Em         **
After leaving      my apartment
A          ***     Bm*
I feel this        cold inside me

On my way to your apartment
I write for fear of silence
You carved a boat to sell my shadow
A             Bm*    A  A  A 
Now I walk alone

(keep playing A and gradually increase the intensity of the sound up to where they 
introduce a new set of chords)

Bm     Am7      Em/G     G

Bm            Am7              Em/G            G
I hit the sidewalk and this is how it starts
Bm            Am7                  Em/G           G
Hide in a raincoat when things are falling apart

Bm* F#m7
Bm* F#m7

Bm*           Em           A           Bm*


Bm*           *    Em         **
After leaving      my apartment
A          ***     Bm*
I hear the         coast by nightfall
So sure to keep you dreaming
You understood
Oh, I know you understood
Bm*         Em      A      Bm*   A    A    A    A
Yes sir, it shows I was no good   alright, alright

Bm            Am7              Em/G            G
I hit the sidewalk and this is how it starts
Bm            Am7                  Em/G           G
Hide in a raincoat when things are falling apart
Bm            Am7                  Em/G           G
Cause sooner or later this is bound to stop
Bm            Am7                  Em/G           G
Come on, let's savor what we're falling over

Bm            Am7                  Em/G           G (2x)

Bm*           *    Em         **   A          ***     Bm


Bm*           *    Em         **
After leaving      your apartment
A          ***     Bm
I hear the         coast...

this is pretty much most of the song, they have a bunch of guitars 
so unless you have a band, this works for the background guitar.