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Chord diagram for C
Chord diagram for E7
Chord diagram for F
Chord diagram for G
Chord diagram for Am
      https://www.youtube.com/watch?v=6CM5coW7Lkg

It looks like he's playing the below chords, and to me it sounds correct with a capo on the second fret
although the video shows one on the third fret (maybe he's tuned a half step down?)

I'm pretty confident about everything except the E7, if anyone thinks it's something else please let me know!

[Intro]
C E7 F C

[Verse 1]
C                       E7
all these lines on our face

growing deeper
F                               C
   all these aches and these pains
        G
make use weaker
F                    C
all these years gone by
E7                         F
   and it's never felt so right

[Chorus]
F                               C
just like George Burns and Gracie Allen
      Am                                F
just like Johnny Cash and June Carter, too
F                 C
getting old is a priviledge we hold
           G                 F         C
And I'm so lucky I'm getting old with you

[Verse 2]
C                               E7
all the memories that we made together
F                            C
erase these lines aches and pains
                G
and make us better
F                    C
all this time gone by
E7                           F
     and it's never felt so right

[Chorus]
F                               C
just like George Burns and Gracie Allen
Am                                      F
just like Johnny Cash and June Carter, too
F                 C
getting old is a priviledge we hold
           G                 F         C
And I'm so lucky I'm getting old with you

[Bridge]
G               F
please take me first
        C
or at least,
           F
spare the curse
        C           G      C
of a long,     and lonely wait

[Chorus]
F                               C
just like George Burns and Gracie Allen
Am                                      F
just like Johnny Cash and June Carter, too
F                 C
getting old is a priviledge we hold
           G                 F         C
And I'm so lucky I'm getting old with you
    

Source: https://tabs.ultimate-guitar.com/tab/yarn_us_brooklyn_ny/take_me_first_chords_2420141

More songs by Yarn (US, Brooklyn, NY)