1. Place peanut butter and butter in the large bowl of a sturdy stand mixer. Beat on medium speed until very smooth, scraping sides of bowl as needed. Gradually beat in confectioners' sugar until smooth.
2. Roll mixture into 1-inch balls. Arrange balls on waxed paper-lined trays or baking sheets. Cover and chill for 3 hours or overnight.
3. In a small, heavy saucepan, melt chocolate chips and shortening over medium-low heat, stirring frequently. Keep warm over very low heat. Remove about one-fourth of the peanut butter balls from the refrigerator. Use a toothpick to hold a peanut butter ball and lower it into the chocolate, leaving the top exposed so that it looks like a buckeye. Allow excess chocolate to drip off.
4. Place ball, undipped portion up, on waxed paper-lined tray or baking sheet. Repeat with remaining peanut butter balls until all are dipped. Chill for 30 minutes, or until firm. Store in the refrigerator. Makes 90 cookies.
5. Makes 90 cookies.