Preheat the oven to 350 degrees F. Grease a 4-inch x 8-inch loaf pan with non-stick cooking spray. Set aside.
In a large mixing bowl, combine the mashed banana and melted butter. Stir in the sugar, egg, and vanilla.
In a medium mixing bowl, stir together the flour, baking soda, and salt. Add the dry ingredients to the wet ingredients and mix until just combined.
Add the peanut butter and chocolate chips to the bowl and stir into the batter. Pour the batter into the greased loaf pan. If desired, top the bread with a few more peanut butter and chocolate chips.
Bake for 50 to 70 minutes or until a toothpick inserted into the center comes out clean.
Remove the bread from the oven and allow it to cool on a wire rack for 5 minutes. Then, remove the loaf from the pan and cut into slices for serving.