the song doesn't really sound like it has chords in the verses, these ones work 
quite well, play each one for a beat

Chris Cornell - Part of Me

C#m     G#  A G#             C#m        G# A G#
Little girl I love when she talks to me
Got the smile and she walk that walk with me
I want the girl but I want a lot
Might cross my mind but that's where it stops

[Chorus]
C#m                G#          F#m                   G#
That bitch ain't a part of me, no that bitch ain't a part of me
I said no that bitch ain't a part of me, no that bitch ain't a part of me
I said no that bitch ain't a part of me, no that bitch ain't a part of me
I said no that bitch ain't a part of me, no that bitch ain't a part of part of part of OWW

I love the girl, I'm loving the dress she wears
She's got a hold, got a hold of my neck oh yeah
I wanna cry; the way that she moves
I want the girl but not what she's going through

[Chorus]

She was so friendly
I had one too many
And now that they tell me
She was rubbing up against me
But I swear it never meant a thing
She was just a fling
There's no other woman who does it like you

[Chorus]