In a medium saucepan, melt the butter over low heat. Add the chocolate chips and peanut butter and whisk until smooth. Remove from the heat and pour into an 8-inch square baking dish. Refrigerate until firm, about 45 minutes.
Place the chopped peanuts on a large plate. Drop teaspoons of the chilled chocolate mixture onto the plate and roll them in the peanuts until coated. Roll briefly between your palms to form balls (if the mixture becomes too soft, refrigerate between batches). Refrigerate the bites in an airtight container.