Okay, guitar-wise, there isn't a terrible lot to the actual recording. Annie simply does a simple
pitch-shifted lick for pretty much the entire first part of the song. The actual guitar parts can be
found at this person's tab; they seem correct: 
http://tabs.ultimate-guitar.com/s/st_vincent/huey_newton_tab.htm 

What I've figured out are the chords that the keyboard is playing underneath it. I'm pretty sure
I've got it at least in the right neighborhood.

Em       Em7
Feelings flash cards
Cmaj7    Adim
Fake knife real ketchup
D        Bm
Cardboard cutthroats
Gmaj7    Cdim
Cowboys of information
Em       C#dim7       Em       C#dim7
Pleasure dot loathing dot Huey dot Newton
Em       Cdim
Oh, it was a lonely, lonely winter

n/c (brief drum interlude)

G        Em7/G
Fuckless pawn sharks
G        B/G**
Toothless but got a big bark
Am       Am7
Live children blind psychics
Am(add9) B/A
Turned online assassins
G        G7        Am/G       Gsus2    
So Hale-Bopp, Hail Mary, hail Hagia Sophia
G                  Gsus4(add2)
Oh it was a lonely, lonely winter

(the rest is with that killer guitar riff, so these chords aren't really utilized, but these are the
bass notes, I guess)

Em
Entombed in the shrine of zeros and ones
You know, you know
With fatherless features, you motherless creatures you know
In perpetual night oh it's terribly frightening
You know, you know
You got the pop and the hiss in the city of misfits you know
B5                    A5                       Em 
Safe safe and safest, faith for the faithless
Dim dim and dimmer succor for sinners


**the G bass note on this B chord is very brief, and the B chord is left to ring out.