OK so there is a tab for this song already on Ultimate guitar, however unless you're 
playing power chords the whole time it is all bar chords. I think this version is 
just a bit easier to 
play!! Here it is:

Capo 1

(intro)

F

(chorus)

F
Gravity
                Dm
Don't mean too much to me
             Bb
I'm who I've got to be
                C
These pigs are after me,
A7
After you
Dm
Run away
             F
Like it was yesterday
             Bb
And we could run away
            C#
If we could run away
Eb             F
Run away from here.

(break)

F       C    Bb    C
F       C    Bb    C
Dm   C    Bb    C
F       Fb     F

(verse1)

(pause)                F
I've got a bulletproof heart
Bb             C             F
You've got a hollow-point smile
Bb             C         Dm
Me and your runaway scars
                  Bb
Got a photograph dream
       C         F      Fb  F
On the getaway mile
(pause)                   F
Let's blow a hole in this town!
Bb         C                F
And do our talking with a laser beam
Bb     C            Dm
Gunning out of this place
              Bb
In a bullet's embrace
            C       F
Then we'll do it again.

(prechorus)

F         C    Dm
How can they say
                 F        Bb
"Jenny could you come back home?"
                  C         Dm
'Cause everybody knows you don't 
              F
Ever wanna come back
Bb             C
Let me be the one to save you

(chorus)

F
Gravity
     F/Fb      Dm
Don't mean too much to me
     F     Bb
I'm who I've got to be
                C
These pigs are after me,
A7
After you
Dm
Run away
     C/Fb    F
Like it was yesterday
             Bb
And we could run away
            C#
If we could run away
Eb             F
Run away from here.

(guitar break/solo)

F     C     Bb     C
F     C     Bb     C
Dm C     Bb     C
F     Fb     F

(verse2)

                           F
I'm shooting out of this room
Bb        C                      F
Because I sure don't like the company
Bb         C                 Dm
Stop your preaching right there
                       Bb
'Cause I really don't care
         C      F     Fb    F
And I'll do it again
F
So get me out of my head
Bb          C               F
'Cause it's getting kind of cramped, you know
Bb      C        Dm
Coming ready or not
                     Bb
When the motor gets hot
       C        F
We can do it again

(prechorus)
    F C/Fb  Dm
The papers say
                  F        Bb
"Johnny won't you come back home?"
                  Dm        Gm
'Cause everybody knows you don't
Am
Want to give yourself up
Bb                 C
Tell the truth and God will save you!

(chorus)

F
Gravity
     F/Fb      Dm
Don't mean too much to me
     F     Bb
I'm who I've got to be
                C
These pigs are after me,
A7
After you
Dm
Run away
     C/Fb    F
Like it was yesterday
             Bb
And we could run away
            C#
If we could run away
Eb             F
Run away from here.

(break)

F     C#     F     C#     Ab

(bridge)
    F
And though I know 
     C#
How much you hate this
F
Are you gonna be 
    C#
The one to save us
Ab
From the black
     Eb
And hopeless feeling?
C#
Will you mean it
          Eb
When the end comes reeling?
F
Hold your heart
 C#
Into this darkness
F                   C#
Will it ever be the light
              Ab
To shine you out
            Eb
Or fail and leave you stranded?
C#
I ain't gonna be
     Eb
The one left standing
C#
You ain't gonna be
     Eb
The one left standing
C#
We ain't gonna be 
     Eb
The ones left standing

(chorus)

(pause)  F
Gravity
     (Pause)             Dm
Don't mean too much to me
             Bb
Is this our destiny?
               C
This world is after me,
A7
After you
Dm
Run away
     C       Bb 
Like it was yesterday
     C       Dm
And we could run away
Dm         Bb
Run away, run away
C              F
Run away from here

(outro)

F C Bb C
       Yeah
F C Bb C
     Away from here
Dm C Bb C F
   Away from here