[Song on YouTube] All the tabs I could find were crap, so I wrote up a guitar arrangement. The inverted voicings in the choruses made it tough to figure out, but capoing the 2nd fret gets it pretty close.

Capo 2nd fret. / = 1/4 note

V1)
  A    3-5-5-4-3-x  (2 bars) As logic stands you couldn't meet a man who's from the
  G#m  2-4-4-2-2-x  (2 bars) future.
  A    3-5-5-4-3-x  (2 bars) But logic broke as he appeared he spoke about the
  G#m  2-4-4-2-2-x  (2 bars) future.
  B    5-7-7-6-5-x  (1 bar)  "We're not gonna
  A    3-5-5-4-3-x  (1 bar)  make it."
  B    5-7-7-6-5-x  (1 bar)  He explained how the
  A    3-5-5-4-3-x  (1 bar)  end will come.
  A    3-5-5-4-3-x  (2 bars) You and me were never meant to be part of the
  G#m  2-4-4-2-2-x  (1 bar)  future.
  B          x-0-7-6-5-x  / /
  Bsus4add9  x-0-x-4-3-x  /
  Bmaj7      x-0-6-6-5-x  /

C)
  Amaj7      3-2-0-0-0-2  (1 bar)     All we
  Dmaj7/F#   0-3-2-0-0-0  (1 bar)  have     is
  C#m7/G#    2-2-4-2-3-2  (1 bar)  now.
  F#7sus4    0-x-2-2-3-x  / /
  F#         0-x-2-1-0-0  / /

  All we've ever had is now.
  All we have is now.

  Amaj7      3-2-0-0-0-2  (1 bar)    All we've
  Dmaj7/F#   0-3-2-0-0-0  (1 bar)  ever had     i-
  G#m7       2-4-2-2-2-2  (2 bars) is now.

B1)
  F#m7       0-2-2-0-3-x  (1 bar)
  B7         x-0-2-0-2-0  (1 bar)

V2)
  I noticed that he had a watch and hat that looked familiar.
  He was me from a dimension torn free of the future.
  "We're not gonna make it." He explained how the end will come.
  You and me were never meant to be part of the future.

C)

B2)
  F#m7       0-7-5-7-x-x  (2 bars)
  Emaj9      x-5-4-6-5-x  (2 bars)
  D9-5       8-x-8-7-7-x  (2 bars)
  A          3-x-0-0-0-3  (2 bars)
  Bm6/F#     0-0-2-2-1-2  (1 bar)
  E7/G#      2-0-0-2-1-2  (1 bar)

Outro)
  Amaj7      3-2-0-0-0-2  (1 bar)     All we
  Dmaj7/F#   0-3-2-0-0-0  (1 bar)  have     is
  C#m7/G#    2-2-0-2-0-x  (end)    now.
  ...
  C#m9       x-2-0-2-2-x  (organ adds D#)
  ...
  C#m11      x-2-0-2-2-0  (synth adds F#)