The other versions on here are alright (especially Sherkon's, whose template 
I used, and a portion of whose tab I reused here).

But, The Civil Wars play this song in DADGAD, which gives it a very 
different flavor from standard or drop tuning.  It has a lot of cool chords,
and it's generally just a nice tuning to play around with.  The chords are 
simpler, and slightly different from standard tuning.

This song is awesome.

Questions?  Just PM me on UG, or leave a comment.

Song: Falling
Artist: The Civil Wars

Tuning: DADGAD, capo 3

Main riff, 5x:
|--------------------------|
|--------------------------|
|-----0-------0-------0----|
|---4---4---4---4---4---4--|
|-2-----------------------4|
|---------4-------2--------|

Verse first ending:
|------------|-----------|
|---------0--|---------0-|
|---------0--|---------0-|
|------5-----|-------2---|
|----5-------|-----0-----|
|--5---------|-0h2-------|

Main riff, 3x:
|--------------------------|
|--------------------------|
|-----0-------0-------0----|
|---4---4---4---4---4---4--|
|-2-----------------------4|
|---------4-------2--------|

Verse second ending:
|------------|-------0---|
|---------0--|-------0---|
|---------0--|-----6-----|
|------5-----|---7-------|
|----5-------|-0---------|
|--5---------|-----------|

Chorus Chords:
|-0--0--0--0--0-|
|-0--0--0--0--0-|
|-7--6--4--2--1-|
|-x--x--x--0--0-|
|-5--4--2--4--2-|
|----------4--2-|

Chorus ending
|-(0)-(0)-(0)-(0)-(0)-(0)-(0)-|
|-(0)-(0)-(0)-(0)-(0)-(0)-(0)-|
|--4---6---7---6---4---6---7--|
|--0---0---0---0---0---0---0--|
|--x---x---x---x---x---x---x--|
|--5---5---5---5---5---5---5--|

Main riff, 2x:
|--------------------------|
|--------------------------|
|-----0-------0-------0----|
|---4---4---4---4---4---4--|
|-2-----------------------4|
|---------4-------2--------|

Verse (Main riff variation), 3x:
|---------------------------|
|---------------------------|
|---0-0----0-0---0-0----0-0-|
|---4-4----4-4---4-4----4-4-|x3
|-2-------------------4-----|
|--------4-----2------------|

Verse variation, first ending
|--------------|-------------|
|--------------|----------0--|
|----0-0---0-0-|------0-0-0--|
|----4-4---4-4-|------2-2-2--|
|--------------|-------------|
|--5-----5-----|--0h2--------|

Verse (Main riff variation), 3x:
|---------------------------|
|---------------------------|
|---0-0----0-0---0-0----0-0-|
|---4-4----4-4---4-4----4-4-|x3
|-2-------------------4-----|
|--------4-----2------------|

Verse variation, second ending chords:
|-0--0-|
|-0--0-|
|-0--6-|
|-5--7-|
|-5--0-|
|-5----|

Chorus Chords:
                 "Can't help falling out of love..."
|-0--0--0--0--0-|-(0)-(0)-(0)-(0)-(0)-|
|-0--0--0--0--0-|-(0)-(0)-(0)-(0)-(0)-|
|-7--6--4--2--1-|--4---6---7---6---6--|
|-x--x--x--0--0-|--0---0---0---0---7--|
|-5--4--2--x--x-|--x---x---x---x---0--|
|----------4--2-|--5---5---5---5------|

                  "...liar..."
|-0--0--0--0-(0)-0-|-(0)-(0)-(0)-|
|-0--0--0--0-(0)-0-|-(0)-(0)-(0)-|
|-7--6--4--2-(2)-1-|--4---6---6--|
|-x--x--x--0-(0)-0-|--0---0---7--|
|-5--4--2--4-(x)-2-|--x---x---0--|
|----------4-(3)-2-|--5---5------|

                  "Can't help falling..."
|-0--0--0--0--0-|-(0)-(0)-(0)-(0)-(0)-(0)-(0)-|
|-0--0--0--0--0-|-(0)-(0)-(0)-(0)-(0)-(0)-(0)-|
|-7--6--4--2--1-|--4---6---7---6---4---6---7--|
|-x--x--x--0--0-|--0---0---0---0---0---0---0--|
|-5--4--2--4--2-|--x---x---x---x---x---x---x--|
|----------4--2-|--5---5---5---5---5---5---5--|

Main riff outro, 4x:
|--------------------------|
|--------------------------|
|-----0-------0-------0----|
|---4---4---4---4---4---4--|
|-2-----------------------4|
|---------4-------2--------|