In a large bowl, mix together peanut butter, butter, and vanilla until smooth.
Add confectioner's sugar to the peanut butter 1 cup at a time. Mix until almost combined after each addition. Continue until all sugar has been incorporated. The peanut butter mixture should have a dough-like texture and not be too sticky.
Roll peanut butter mixture into balls (1 level tablespoon - about the size of a small bouncy ball). Place peanut butter balls onto a baking sheet lined with a silicone mat, waxed paper, or parchment paper. Chill peanut butter balls for 30 minutes to 1 hour.
Place a glass bowl over a medium saucepan with 1 to 2-inches of simmering water. Add the chocolate chips and paraffin wax to the bowl. Stir occasionally until everything is melted and the wax is mixed in.
Insert a toothpick into the center of one peanut butter ball. Use the toothpick to dip the ball into the melted chocolate. Be sure to leave a circle of peanut butter showing at the top of the candy for the signature buckeye look. Let the excess chocolate drip back into the bowl.
Place the candy back onto the lined baking sheet. Repeat with remaining peanut butter balls. Refrigerate for 10 minutes or until ready to serve.
Recipe yield varies! I usually get between 50 and 70 buckeyes from this recipe. Yield really depends on how big you make the peanut butter balls.
Paraffin wax can be found in the canning section of your local grocery store. The wax sets the chocolate at room temperature so you don't have to worry about it melting or waiting for it to harden in the fridge. You can omit the wax if you feel the need to.
If peanut butter "dough" is sticky to the touch, add a couple tablespoons of powdered sugar and mix until desired consistency is reached.