Knights of Cydonia is a pretty ridiculous piece of music. Today I finally sat down and listened to the various verses, so here are the chords for future reference:
Em G C G
B C E♭ G
Cm G A♭ E♭
Gm A♭ E♭ G
Cm
Cm E♭ A♭ E♭
G A♭ B E♭
A♭m E♭ E B
E♭m E B E♭
A♭m
G♯m B E B
D♯ E G B
Em B C G
Bm C G B
Em
You may find it convenient to think about the middle verse in terms of sharps instead of flats.