I think this is the way they play it.
I'm sorry for any mistaktes.

No Capo

Chords:
E     x-2-2-1-0-0
A     x-0-2-2-2-0
Am    x-0-2-2-1-0
Ab    4-6-6-5-4-4
C#m   x-4-6-6-5-4
Bm    x-2-4-4-3-2      
A'    5-7-7-6-5-5
Am'   5-7-7-5-5-5
B'    7-9-9-8-7-7

* only one strum


E*
I don't want a lot for Christmas 
E*
There is just one thing I need 
A*
I don't care about the presents 
Am*
Underneath the Christmas tree
E*              Ab*
I just want you for my own 
C#m*                Ab*
More than you could ever know 
E*                C#m*
Make my wish come true 
A*             Am*
All I want for Christmas 

E
I don't want a lot for Christmas 
E
There is just one thing I need
A
I don't care about the presents 
Am
Underneath the Christmas tree 
E
I don't need to hang my stocking 
E
There upon the fireplace 
A
Santa Claus won't make me happy 
Am
With a toy on Christmas day 

E               Ab
I just want you for my own 
C#m                 Ab
More than you could ever know 
E                 C#m
Make my wish come true 
A              Am            E
All I want for Christmas is you 
C#m  Bm*
You Baby

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

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

E                      Ab
'Cause I just want you here tonight 
C#m            Ab
Holding on to me so tight 
E               C#m
What more can I do 
A              Am            E
All i want for Christmas is you
C#m  Bm*
You Baby

Ab
Oh, all the lights are shining 
 C#m
So brightly everywhere 
Ab
And the sound of childrens' 
C#m
Laughter fills the air 

A'
And everyone is singing 
Am'
I hear those sleigh bells ringing 

Santa won't you bring me 

The one I really need 
          B'
Won't you please bring my baby to me

E
I don't want a lot for Christmas 
E
This is all I'm asking for 
A
I just wanna see my baby 
Am
Standing right outside my door 

E*              Ab*
I just want you for my own 
C#m*                Ab*
More than you could ever know 
E*                C#m*
Make my wish come true
A*             Am*           E*
All I want for Christmas is you
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