I'm not a musician, so consider this a 1st stab at it. I'm especially unsure of the Bm on "eyes", but it was my best guess. Also, there might be a good internal chord during the 1st 4 lines, but I didn't find it.
And you can see I don't get to what I think might be a key change at the end of the 3rd verse.
So, it's just a start.
I love this song and look forward to seeing people's improvements/confirmations on these chords!

F - Outside (through) alive. We
G - went to see some C- friends of his who
F- lived upon a G- farm. Strange and gentle
C- country folk who'd F- wish nobody
G -harm. Fresh cut sixty C- acres
F - eight cows in the G- barn. But the
F - thing that I re C- member on that
G - cold day in De F-cember, was that my
Bm - eyes they did brim C- over as we
F - talked