I took the liberty to "correct" the already submitted chords by "silencekiller", 
so all the credits for the original version belong to him!

INTRO: Bm - G - Bm - G

VERSE 1:
        Bm
I don't mind,
          G
If your hand's a little cold.
           Bm
Cause I'm alive,
       G
But I got nowhere to go.

CHORUS:
    Bm            E
So stay with me Evelyn.
       Bm                 E
Don't leave me with the medicine.

VERSE 2:
        Bm
In the night
        G
As you sit and watch me sleep
            Bm
I know you cry
        G
But I never want to see.
          E
So if you go
                       A
I don't know what I'll do.
             E
So don't you go
                           A
Cause I've got no one but you.

CHORUS:
    Bm           E
So stay with me Evelyn.
        Bm                E
Don't leave me with the medicine.
    Bm            E
So stay with me Evelyn.
       Bm                E
Don't leave me with the medicine.

INTERLUDE: Bm - A - E - G[x4]

VERSE 3:
           Bm     A
I see the lights
          E             G
Casting shadows on my screen.
            Bm   A
And I don't mind
         E                G
The lullabies from the machines.
           E
But if you go
                       A
I don't know what I'll do.
             E
So don't you go
                          A
Cause I've got no one but you.

CHORUS:
    Bm    A       E    G
So stay with me Evelyn.
      Bm     A           E    G
Don't leave me with the medicine.
   Bm    A       E    G
So stay with me Evelyn.
      Bm     A      E      G
Don't leeee-eaaave me.

INTERLUDE: Bm - A - E - G [x2]

OUTRO:
    Bm       A             E        G
I'm more afraid than I've ever been,
   Bm    A       E       G       Bm
So stay with me Evelyn.