In a large mixing bowl, beat 1½ cups peanut butter, ½ cup softened butter, and ½ teaspoon vanilla extract on medium speed until light and fluffy.
Gradually add 4 cups powdered sugar, mixing a little at a time until completely incorporated and the mixture forms a soft dough.
Cover and refrigerate the peanut butter mixture for 30 minutes.
Line a baking sheet with parchment paper. Roll the chilled mixture into 36 evenly sized balls and place them on the prepared baking sheet.
Refrigerate the peanut butter balls for another 30 minutes to firm them up.
Place 3 cups semi-sweet chocolate chips and 1 tablespoon coconut oil in a microwave-safe bowl. Microwave at 50% power for 1 minute. Stir well, then continue microwaving in 30-second intervals, stirring after each interval, until the chocolate is completely melted and smooth.
Insert a toothpick into each peanut butter ball. Dip each ball into the melted chocolate, leaving a small portion of the peanut butter filling exposed at the top.
Place the dipped balls back on the parchment-lined baking sheet. Carefully remove the toothpick and use your finger or a small spoon to smooth over the hole.
Refrigerate the peanut butter balls until the chocolate is completely set.
Store covered in the refrigerator until ready to serve.