Preheat the oven to 350°F. Grease a loaf pan or line with parchment paper.
Mash the bananas in a large bowl until almost smooth. Stir in the peanut butter and vanilla extract until well combined.
Add the oats, salt, and baking powder to the banana mixture and mix thoroughly. Fold in 1/3 cup of the chocolate chips, reserving the rest for topping.
Pour the mixture into the prepared loaf pan and smooth the top with a spoon or spatula. Sprinkle the remaining chocolate chips over the top.
Bake for 25-30 minutes, or until a knife inserted in the center comes out clean. Allow to cool before slicing into 6-8 bars.