Hi! I know that the finger-picking style actually used in the song is more 
complicated but I put this together for those who just want to strum along.

Intro: 

Am Em C G C

Verse:

Am       Em
Now I see winter's dawn

C        G             C
The wind turns traitor cold

Am         Em
Seems long since summer time

C               G         C
And the stories that were told

Am          Em
We spoke of dreams that came

C     G       C 
To us when we were young

Am         Em
But as the morning rose

C        G           C
We spoke with forked tongues


Chorus:

Dm           G
My love is a fleeting one

Dm              G
My man could be anyone

C        F Dm     G
And our love is a setting sun


Verse:

Am               Em
As we took those evening walks

C           G        C
Down through the graveyard

Am          Em
Those names engraved always

C               G     C
Put a new shade to my thoughts

Am            Em
But he and I, we both knew

C         G       C
The bread that we break

Am          Em
Would never take their place

C               G        C
What's cold, you mustn't await


Chorus:

Dm           G
My life is a fleeting one

Dm             G
My work is just a web I've spun

C     F Dm     G
Oh my life is a setting sun


Bridge:

Em          Am
I don't know where I'm going

C                     Em
But no one is coming with me

Em                     Am
I won't give up chasing love, son

C                    Em
Here I go, look at me run

F
Here I go

        G
Look at me run

F
Here I go

        G
Look at me run


Chorus:

Dm           G
My love is a fleeting one

Dm              G
My man could be anyone

C        F Dm     G
And our love is a setting sun


Dm           G
My life is a fleeting one

Dm             G
My work is just a web I've spun

C     F Dm     G
Oh my life is a setting sun


End verse:

Am          Em
Baffled by the lies we blamed

C      G          C
We met the end too soon

Am           Em
I was honest when I told you

         C       G  C    
We're as cryptic as the moon