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

Here is Why You Need An Adapter

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

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L

Chile

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

Type C

Type L