You Do Need power plug adapter while traveling from British Virgin Islands to Chile.

Here is Why You Need An Adapter

The outlet and plug type used in Chile are C and L and in British Virgin Islands are A and B. This is how they look like.

British Virgin Islands

In British Virgin Islands, outlets of type A and B are in use.

Type A

Type B

Chile

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

Type C

Type L