In a medium-size bowl, blend the butter, peanut butter, and confectioners’ sugar until smooth. (You may need to adjust the amount of sugar depending on the brand of peanut butter you use. Jif extra crunchy works perfectly with the measurements given.) Roll into 1-inch balls. Chill thoroughly.
Melt the chocolate chips, semisweet chocolate, and paraffin in the top of a double boiler or a pan set over hot water (the water should not boil). Use a small-bottomed pan, which will keep the chocolate deep for dipping. Using a toothpick or thin skewer, dip the peanut butter balls in the melted chocolate. Leave an “eye” undipped at the top of the ball so that it resembles a buckeye. If the coating is thick, you might have to prepare a second batch of chocolate. Chill to set the chocolate.
Ruth Cahill has made thousands of buckeyes over the years. For winning a blue ribbon at the Ohio State Fair, she was one of a handful of cooks invited to New York for the Citymeals-on-Wheels benefit, where bakers made 500 of her buckeyes as part of the fundraising dinner.