Some of the chords on this site sound excellent played by themselves,
 but they were not close enough to the original.
Others were exactly (or almost) like the synth in the song,
but not "full" enough to play as an acoustic "guitar+voice" kind of thing.

So this is my attempt at having both fidelity and a fuller sound.
For the synth tab, thanks to Gallagher2006
http://tabs.ultimate-guitar.com/r/radiohead/idioteque_ver2_guitar_pro.htm
I've basically just re-tabbed the synth for guitar.

-------CAPO 3--------

Cm7/E Cm7/G  Em     G
E|-(0)---(0)----3-----7--|
B|--1-----0-----5-----3--|
G|--0-----4-----4-----0--|
D|--2-----2-----2-----5--|
A|--2-----3-----x-----x--|
E|--0-----3-----x-----x--|
(Notes in brackets, I think it sounds better if you don't play them,
so that the right changes are accentuated in each passage, but you can if you wish)

Alternative forms for the chords: You can use whichever you think sounds best and/
or is easier to play.

C7M/E: 0 2 2 5 x(0)
C7M/G: 3 3 2 4 0(0)
Em:    0 2 2 0 0 3
G:     x x 5 7 x 7

Intro:
Cm7/E    Cm7/G    Em (022000@1)  G (320003@1)Verse:
Cm7/E             Cm7/G
Who's in a bunker? Who's in a bunker?
Em (022000@1)                GWomen (320003@1)and children first, and the children first, and the children...
Cm7/E              Cm7/G
I'll laugh until my head comes off
Em (022000@1)              GI (320003@1)swallow till I burst,  until I burst, until I
Cm7/E            Cm7/G
Who's in a bunker, who's in a bunker
Em (022000@1)            GI've (320003@1)seen too much, I haven't seen enough, you haven't seen enough
  Cm7/E            Cm7/G
I'll laugh until my head comes off
Em (022000@1)                 GWomen (320003@1)and children first, and children first, and children

Chorus:
Cm7/E     Cm7/G    Em (022000@1)                   GHere (320003@1)I'm alive... everything all of the time
Cm7/E     Cm7/G    Em (022000@1)                   GHere (320003@1)I'm alive... everything all of the time

Verse 2:
Cm7/E           Cm7/G
Ice age coming, Ice age coming
Em (022000@1)              GLet (320003@1)me hear both sides, Let me hear both sides, Let me hear both
Cm7/E           Cm7/G
Ice age coming, Ice age coming
Em (022000@1)              GThrow (320003@1)it in the fire, Throw it in the fire, Throw it on the
Cm7/E         Cm7/G
We're not scaremongering
Em (022000@1)            GThis (320003@1)is really happening, Happening
Cm7/E         Cm7/G
We're not scaremongering
Em (022000@1)            GThis (320003@1)is really happening, Happening
Cm7/E             Cm7/G
Mobiles squirking, Mobiles chirping
Em (022000@1)                GTake (320003@1)the money and run, Take the money and run, Take the money

Chorus:
Cm7/E     Cm7/G      Em (022000@1)                GHere (320003@1)I'm alive... everything all of the time
Cm7/E     Cm7/G      Em (022000@1)                GHere (320003@1)I'm alive... everything all of the time

Outro:
Cm7/E    Cm7/G    Em (022000@1)  G