I did this by ear, so it might not all be correct but I played it with the track 
and it sounds right! 

But if you hate barre chords as much as me you can put a capo on 2nd and get rid 
of barring F#m and B, and change the chords to;

E - D
F#m - Em
G#m - F#m
A - G
B - A
D - C
Eb - C#

This is a beautiful song I hope you enjoy playing it!

Intro- E G#m E G#m

Verse 1 

  E        G#m       E              G#m
Children sleeping, snow is softly falling
F#m          Eb    F#m                A      B
 Dreams are calling like bells in the distance
 E        G#m      E       G#m
 We were dreamers not so long ago
F#m         Eb    F#m         A     B
 But one by one we all had to grow up
G#m                           A
 When it seems the magic's slipped away
    D                             B
 We find it all again on Christmas day

 E                    F#m
Believe in what your heart is saying
  E            A
 Hear the melody that's playing
  E                B
 There's no time to waste
   F#m               A     B
 There's so much to celebrate
  E                  F#m
 Believe in what you feel inside
 E                       G#m     C#m
And give your dreams the wings to fly
  F#m                        B
 You have everything you need 
  (N.C.)
 If you just believe

 E          G#m      E               G#m
Trains move quickly to their journey's end
 F#m       Eb   F#m        A      B
 Destinations are where we begin again
 E        G#m      E             G#m
 Ships go sailing far across the sea
 F#m        Eb     F#m           A            B        
 Trusting starlight to get where they need to be
 G#m                               A
 When it seems that we have lost our way
  D                               B
 We find ourselves again on Christmas day
 
 E                    F#m
Believe in what your heart is saying
  E            A
 Hear the melody that's playing
  E                B
 There's no time to waste
   F#m               A     B
 There's so much to celebrate
  E                  F#m
 Believe in what you feel inside
 E                       G#m      C#m
And give your dreams the wings to fly
  F#m                        B
 You have everything you need 
 A           E      F#m
If you just believe 
E                   F#m
If you just believe 
E                   F#m
If you just believe 
E                  F#m
If you just believe 
A            E
Just believe