Preheat the oven to 350 F. In a large bowl, combine butter with powdered sugar until fluffy. Add in the vanilla extract, and mix until smooth. Add in the flour, and mix until it is fully combined.
Fold in the cocoa pebbles cereal and chocolate chips. Roll the cookie dough into balls, and place onto a large ungreased baking sheet. Bake for 10-12 minutes. In a shallow dish, place the powdered sugar.
Roll each cookie into the powdered sugar.