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

Here is Why You Need An Adapter

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

Denmark

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

Type C

Type E

Type F

Type K

Chile

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

Type C

Type L