Insert popsicle stick into each banana piece.
Place the chocolate chips in a small microwave safe bowl. Microwave on high for 1 to 2 minutes, or until smooth; stopping to stir every 25 seconds (or use a double boiler to melt the chocolate). If chocolate is too thick, microwave it a little more.
One by one, dip each piece into melted chocolate, spooning on additional chocolate to cover. Then immediately sprinkle each banana with chopped peanuts and set on a baking sheet with waxed paper. Refrigerate until chocolate is firm, about 25 minutes. Store in refrigerator up to 2 days.