this is how i believe Elvis plays the song in the 1968 comeback special... enjoy
F
Well, it's Christmas time pretty baby 
                        C 
and the snow is falling on the ground 
           F
Well, it's Christmas time pretty baby
                       C
And the snow is falling down 
             G7
Well you be a real good little girl    
F                                      C
Santa Claus is back in town
C 
Got no sleigh with reindeer
C
No sack on my back
C                                                  C7
You're gonna see me comin' in a big black caddilac
F
Oh, it's Christmas time pretty baby
                      C
And the snow is falling on the ground
                G7
Well you be a real good little baby
F                                      C
Santa Claus is back in town  
C
hang up  your pretty stockings   
C
turn off the light
C                                  C7
santa clause is coming  down your chimney tonight
      F
oh, it' christmas time pretty baby
                      C
and the snow is falling on the ground
                 G7
well you be real good little baby
F
santa clause is back in town

来源：www.ultimate-guitar.com