This is the song Be My Baby by the Ronnettes, released in 1963, produced by Phil Spector. There are a few 7th chords, and one Barre chord, but they're easy enough to do along with the standard chords. 

Chords used

C  032010
D  xx0232
Dm xx0231
G  320033
G7 320001
E  022100
E7 020100
A  002220
A7 002020
F  133211

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Capo 4th Fret



Verse

C                          Dm        G7
The night we met I knew I, needed you so.
C                           Dm           G7
And if I had the chance I'd never let you go
E             E7               A            A7
So won't you say you love me; I'll make you so proud of me.
D                D7                G            G7
We'll make them turn their heads every place we go.

Chorus
             C
So won't you please (Be my be my ...)
Am
Be my little baby (My one and only...)
F
Say you'll be my darlin' (Be my be my...)
           G7
Be my baby now . Oh ho ho ho

Verse

C                          Dm           G7
I'll make you happy baby, just wait and see,
C                           Dm             G7
for every kiss you give me, I'll give you three.
E              E7            A             A7
Oh, since the day I saw you, I have been waiting for you,
D           D7             G     G7
You know I will adore you till eternity.


Chorus
      
       C
So won't you please (Be my be my ...)
Am
Be my little baby (My one and only...)
F
Say you'll be my darlin' (Be my be my...)
           G7
Be my baby now . Oh ho ho ho  

C
So won't you please (Be my be my ...)
Am
Be my little baby (My one and only...)
F
Say you'll be my darlin' (Be my be my...)
           G7
Be my baby now . Oh ho ho ho
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