In a large bowl, mix together peanut butter, butter, vanilla, and confectioners' sugar using your hands. It will be dry and crumbly at first, but keep working it until everything is very evenly mixed.
Form into 3 large balls, cover with plastic wrap and refrigerate for 30 minutes.
Shape into balls using a scant tablespoon of mixture for each ball and rolling it in your hands to smooth. Place on a baking sheet lined with wax paper.
Refrigerate for at least an hour.
In a small, heavy-bottomed saucepan melt chocolate chips and shortening over low heat, stirring constantly. When smooth, remove from heat.
Use a toothpick to dip each ball into chocolate mixture and place back on baking sheet.
Refrigerate until chocolate is set. Use the back of a spoon to smooth over toothpick holes.
Notes
Makes approximately 3 dozen balls. Store in refrigerator.Chocolate melting wafers can be used instead of the chocolate chips and shortening.