You Do Need power plug adapter while traveling from Saint Kitts and Nevis to Chile.

Here is Why You Need An Adapter

The outlet and plug type used in Chile are C and L and in Saint Kitts and Nevis are D and G. This is how they look like.

Saint Kitts and Nevis

In Saint Kitts and Nevis, outlets of type D and G are in use.

Type D

Type G

Chile

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

Type C

Type L