This song is beautiful and when I play it it's either on a bass, or acoustic guitar. 
lightly with a thumb and palm muted on an acoustic gets almost the same weighty bass sound 
the recording and is very simple to play. I'm about 95% sure this is accurate.

Tuned down to drop D.

Verses
e|---------------------------------------------------------------|
B|---------------------------------------------------------------|
G|---------------------------------------------------------------|
D|---------------------------------------------------------------|
A|-----0---------------0---------------------0-2-------------0-2-|
D|-0-2----0-2-4----0-2-----0-2-4----5-4-0--0--------5-4-0--0-----|

Chorus
e|-----------------------------------------------|
B|-----------------------------------------------|
G|-----------------------------------------------|
D|-----------------------------------------------|
A|-5--5-5-----3---3-3----------------------------|
E|--0------0----0------0--5-0-5-5--0--5-0-5-5--0-|

Ending
e|------------------------------------|
B|------------------------------------|
G|------------------------------------|
D|-----4-5------4-5------5-7------5-7-|
A|---0--------0--------5--------5-----|
E|-0--------0--------5--------5-------|

Other work by Kate Havnevik can be found at: www.katehavnevik.com