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

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G 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

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G