This is the way Mr Leto plays it live on the acoustic guitar.
It's basically this:

in 4/4
Verse:  Gm Gm Fm Fm
Chorus: Gm Gm Fm Fm
        with a variation of Am Am Gm Gm on the higher notes
        and Fm Fm Gm Gm on the "Oooeyoo..." part

strumming: down strokes for the most part, but feel free to get creative.


Verse 1:

Gm                     Fm
No warning sign, no alibi,
                                  Gm
We faded faster than the speed of light
                              Fm
Took our chance, crashed and burned,
No, we'll never ever learn


CHORUS:
Gm       Fm
I fell apart, but got back up again,
Gm       Fm
I fell apart, but got back up again
         Gm       Fm
And then I fell apart, then got back up again

Gm Gm Fm Fm

Verse 2:
We both could see crystal clear
That the inevitable end was near
Made our choice, a trial by fire,
The battle is the only way we feel alive?

CHORUS:
Gm       Fm
I fell apart, but got back up again
Gm       Fm
I fell apart, but got back up again
         Am                 Gm
And then I fell apart, but got back up again,

Fm
Oeyooo, Oeyooo,
Gm
Oeyooo, Oeyooo,
Fm
Oeyooo, Oeyooo,
Gm

Verse 3:
So here we are, witching hour,
The quickest tongue to divide and devour
Divide and devour
If I could end the quest for fire,
For truth, for love, for my desire,
My soul?

CHORUS...

He never quite gets to the 3rd verse and the last chorus live, but you get the point :) 
In the man's own words "take it, modify it, make it your own..."

Use this for reference (if you can stand all the screaming, that is :)) )
http://www.youtube.com/watch?v=NiiKa_l6Rcw