This, I think, is the correct version of the song. 
I'll explain some of the chords for you. Please rate and comment! :-)
Suggestions are very welcome.

Chords:
Eb6: xx1313
B7: x21202
Cm6/Eb: xx1213
E7aug:032130
D11(b9): x55545
B//D#: xx1202
Cm6/Eb: xx1213
Cm6/A: x01013



G
I don't want a lot for Christmas
G/B
There is just one thing I need
C
I don't care about the presents
Eb6
Underneath the Christmas tree


G/D                    B7
I just want you for my own
Em                       Cm6/Eb
More than you could ever know
G/D               E7aug
Make my wish come true
Am7            D11(b9)
All I want for Christmas
   G      Em     C     D   
Is you


G
I don't want a lot for Christmas

There is just one thing I need
C
And I don't care about the presents
Eb6
Underneath the Christmas tree
G
I don't need to hang my stocking

There upon the fireplace
C
  Santa Claus won't make me happy
Eb6
With a toy on Christmas Day

G                      B7/D#
I just want you for my own
Em                      Cm6/Eb
More than you could ever know
G/D               E7aug
Make my wish come true
Am7            D11(b9)      G    Em
All I want for Christmas is you
Am7 D
You baby

Oh I won't ask for much this Christmas
I won't even wish for snow
And I'm just gonna keep on waiting
Underneath the mistletoe

I won't make a list and send it
To the North Pole for Saint Nick
I won't even stay awake to
Hear those magic reindeer click

'Cause I just want you here tonight
Holding on to me so tight
What more can I do?
Baby all I want for Christmas is you
You

Bridge:

B7         
   Oh all the lights are shining
   Em                    
So brightly everywhere
B7 
   And the sound of children's
Em
Laughter fills the air


Cm6/A
   And everyone is singing
G/D            Em
   I hear those sleigh bells ringing
A9
Santa won't you bring me the one I really need?
          C/D
Won't you please bring my baby to me?


Oh I don't want a lot for Christmas
This is all I'm asking for
I just want to see my baby
Standing right outside my door

Oh I just want you for my own
More than you could ever know
Make my wish come true
Baby all I want for Christmas is
You baby

G              Em           Am7 D7
All I want for Christmas is you baby
All I want for Christmas is you baby
All I want for Christmas is you baby