Cut each peeled banana in half lengthwise. Spread each half with peanut butter. Place the banana halves together to make banana "sandwiches." Cut 8 rounds from each banana "sandwich." Place the banana bites on a parchment paper or wax paper-lined baking sheet or tray and freeze for at least 2 hours or overnight.
Place chocolate chips in a microwave-safe bowl and microwave on High, in 15-second increments, until melted (1 to 1 ½ minutes total). Dip half of each frozen banana bite in the chocolate. Let stand until the chocolate is set. If not serving immediately, return to the freezer.
