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

Here is Why You Need An Adapter

The outlet and plug type used in Chile are C and L and in Saint Barthélemy are C and E. This is how they look like.

Saint Barthélemy

In Saint Barthélemy, outlets of type C and E are in use.

Type C

Type E

Chile

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

Type C

Type L