I grew up in Ohio and every Ohioan has a recipe for Buckeyes. The buckeye tree is the state tree but their nuts are poisonous to humans. So, instead, Ohioans decided to make a candy resembling the nut but made with chocolate and peanut butter. Because, you know, chocolate and peanut butter go oh-so-well together and won't poison us.
But... if you are not from the great state of Ohio, then you may refer to these as "chocolate covered peanut butter balls," as I've heard non-Ohioans call them. That's ok. You can call them whatever you like. But in Ohio, they're Buckeyes. And they are beloved by all.
In a mixing bowl, mix together the peanut butter, butter, and vanilla extract until smooth and creamy. Add the powdered sugar (sifted if you so choose) and mix well. Mixture should be creamy but stiff. Roll into 1-inch balls and place on a baking sheet lined with wax paper. Refrigerate for one hour. Melt the chocolate chips and shortening in a double boiler set over hot simmering water. Using a toothpick, dip the balls into the chocolate and then place back on the wax paper. Refrigerate at least another hour before eating.