In a large bowl, beat together the softened butter, peanut butter, and vanilla extract until smooth and creamy. Gradually add the powdered sugar, mixing until a soft dough forms. It should hold its shape but not be crumbly.
Using a tablespoon or small cookie scoop, portion out the dough and roll between your palms into smooth balls about 1 inch in diameter. Place them on a parchment-lined baking sheet.
Pop the tray in the freezer for at least 30 minutes. Cold peanut butter balls are much easier to dip and will hold their shape in the warm chocolate.
Combine the chocolate chips and coconut oil in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until completely smooth and glossy.
Working quickly, use a toothpick or fork to dip each chilled peanut butter ball into the chocolate. Let the excess drip off, then place back on the parchment-lined sheet. For classic buckeyes, leave a small circle of peanut butter showing at the top.
Let the chocolate set at room temperature, or pop them in the fridge for 10-15 minutes to speed things up. Once set, they're ready to eat!