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

Here is Why You Need An Adapter

The outlet and plug type used in Italy are C, F and L 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

Italy

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

Type C

Type F

Type L