I've looked at all of the chord versions of this song 
(all one of them it seems) and it's about 50/50.  I'm 
not saying that what I'm putting down is 100% accurate, 
but at least the first chord of the verse is going to be.  
If you listen to the first day of shooting for the Get 
Back sessions, you can hear George actually explain the 
chord to John. It's a        

B  sus4 6th w3 no5 (looked up the name)

E   4
B   4
G   4
D   2
A   2
E   0

Now onto the song

E7      D7     F#     F    E7
E7      D7     F#     F    E7

B*    Amaj7      B*   Amaj7

B*                                        C           B*   
    Though you sit in another chair, I can feel you here
B*                             C     B*
Looking like I dont care, but I do, I do
D7              C               F#      F
Hiding it all behind anything I see
                  E7
Should someone be looking at me

B*    Amaj7      B*     Amaj7

B*                           C         B*           
While I occupy my mind, I can feel you here
B*                                 C    B*
Love to us is so well timed, and I do, I do
D7                C               F#      F
Wasting away these moments so heavenly
                  E7
Should someone be looking at me

E7           D7                   F#
Let it down, let it all down
         F             E7
Let your hair hang all around me
E7           D7           F#
Let it down, let it down
         F            E7
Let your love flow and astound me

B*   Amaj7      B*      Amaj7

B*                                          C        B*   
While you look so sweetly and divine, I can feel you here
B*                                          C      B*
I see your eyes are busy kissing mine, and I do, I do
D7                 C                     F#      F
Wondering what it is theyre expecting to see
                  E7
Should someone be looking at me

E7           D7                F#
Let it down, let it all down
         F             E7
Let your hair hang all around me
E7          D7               F#          
Let it down, let it down
         F             E7
Let your love flow and astound me
E7           D7           F#     F        E7
Let it down, let it down, ooh (repeat and fade)

Different chords

B  sus4 6th w3 no5   (B*)

E   4
B   4
G   4
D   2
A   2
E   0


Amaj7

E   9
B   9
G   9
D   7
A   7
E   0