Note: In her SXSW performance, Courtney plays all 4 chords in the barred in the F shape:
F: 1st fret    G: 3rd Fret    C: 8th fret    Bb: 6th fret
In other performances she places an open C shape and mostly leaves out the Bb.  
G
I lay awake at four, staring at the wall
F                           C                Bb
Counting all the cracks backwards in my best French
G
Reminds me of a book I skim-read in a surgery
F                      C                          Bb
All about palmistry, I wonder what's in store for me
     G                                  F
I pretend the plaster is the skin on my palms
                             C                     Bb
And the cracks are representative of what is going on
G                                                      F      C
I lose a breath... my love-line seems intertwined with death
                    G
I'm thinking of you too
https://www.coveralia.com/acordes/an-illustration-of-loneliness--sleepless-in-new-york--courtney-barnett.php
G            F           C   Bb
G
I lay awake at three, staring at the ceiling
F                         C                  Bb
It's a kind of off-white, maybe it's a cream
G
There's oily residue seeping from the kitchen
F                               C                                   Bb
It's art-deco necromantic chic, all the dinner plates are kitsch with
G                                                              F
Irish Wolf Hounds, French baguettes wrapped loose around their necks
                    C                   G
I think I'm hungry, I'm thinking of you too
                    F      C  Bb
I'm thinking of you too
                     G  
I'm thinking of you too
                    F      C    Bb
I'm thinking of you too
                       G
I'm thinking of you too