In a large bowl, beat together peanut butter, softened butter, and vanilla extract until the mixture is light and fluffy.
Gradually add the sifted confectioners' sugar, beating continuously until the dough is stiff, firm, and free of lumps. Add up to 2 more cups of sugar if needed to achieve the correct consistency.
Roll the dough into approximately sixty 1-inch balls and place them on wax paper-lined cookie sheets. Insert a toothpick into the top of each ball and chill in the freezer for about 30 minutes until firm.
Melt the chocolate chips using a double boiler or a heatproof bowl set over a pan of simmering water, stirring frequently to achieve a smooth melt.
Holding the toothpicks, dip each chilled peanut butter ball into the melted chocolate, leaving a small circle of peanut butter visible at the top to resemble a buckeye nut.
Place the dipped buckeyes back onto the cookie sheet, carefully remove and discard the toothpicks, and refrigerate until the chocolate is set and ready to serve.