In a large mixing bowl, cream together softened butter, sweetened condensed milk, and vanilla extract.
Gradually mix in powdered sugar until smooth and thick.
Fold in shredded coconut and finely chopped pecans.
Cover and refrigerate for 30 minutes.
Roll the mixture into approximately 1-inch balls and arrange on a wax-paper-lined baking sheet.
Freeze for 30 minutes until firm.
Melt chocolate in a microwave-safe bowl in 30-second intervals, stirring between each interval.
Dip each chilled candy ball into melted chocolate using a fork.
Tap off excess chocolate and place on the lined baking sheet.
Allow the chocolate to set completely before serving or storing.