Cut each banana into three pieces, then insert a popsicle stick into the bottom, stopping before it pokes through.
Pour melted peanut butter into a tall glass and dip each banana, shaking off the excess. Place on a parchment- or silicone-lined baking sheet and freeze for at least 4 hours or overnight.
Once frozen, dip each banana into the melted chocolate, let excess drip off, and return to the baking sheet. Freeze again until the chocolate is set.