Soften the butter, then beat it together with the peanut butter in a medium bowl. Gradually beat in powdered sugar. Mixture may be crumbly, so knead it together a few times with your hands to bring it together.
Scoop out a scant (just less than) tablespoon of peanut butter mixture and roll it into a ball. Place on a cookie sheet lined with parchment paper.
Chill the peanut butter centers until firm - about an hour in the fridge or 5-10 minutes in the freezer. Do not leave in the freezer too long - you want them chilled and firm, not frozen.
Melt the chocolate in the microwave in 30 second intervals, stirring thoroughly between microwaving. Heat until just melted; do not overheat.
Dip each peanut butter center in the melted chocolate to coat it, then place back on the cookie sheet lined with parchment paper. If chocolate starts to harden, microwave for another 15 seconds to warm it back up.
Place dipped peanut butter balls into the fridge for about 10 minutes to set the chocolate. Store at room temp for up to 2 days, or longer in the fridge.