I put down the chords for the first two verses. You just follow this pattern throughout 
song. I have not done the intro or bridge yet, but I will work on it.

B (x2444x@1)              FIf (133211@1)this was the Cold War
A (x02220@1)                     DmWe (xx0231@1)could keep each other warm
F (133211@1)                                    CI (x32010@1)said on the first occasion that I met Marie
B (x2444x@1)                         FWe (133211@1)were crawling through the hatch
A (x02220@1)                      DmThat (xx0231@1)was the missile silo door
F (133211@1)                                                  CAnd (x32010@1)I don't think that she really thought that much of me

Dm (xx0231@1)                        FI (133211@1)never had to learn to love her
Dm (xx0231@1)                      FLike (133211@1)I learned to love the bomb
Dm (xx0231@1)                    F (133211@1)             CShe (x32010@1)just came along and started to ignore me
Dm (xx0231@1)                       FBut (133211@1)as we waited for the big one
Dm (xx0231@1)                     FI (133211@1)started singing her my songs
Dm (xx0231@1)                      F (133211@1)             CAnd (x32010@1)I think she started feeling something for me