You Do Need power plug adapter while traveling from Chile to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Chile are C and L. This is how they look like.

Chile

In Chile, outlets of type C and L are in use.

Type C

Type L

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K