You Do Need power plug adapter while traveling from Chile to Channel Islands (Guernsey & Jersey).

Here is Why You Need An Adapter

The outlet and plug type used in Channel Islands (Guernsey & Jersey) are C and G 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

Channel Islands (Guernsey & Jersey)

In Channel Islands (Guernsey & Jersey), outlets of type C and G are in use.

Type C

Type G