Preheat the oven to 425°F and line a standard 12 cup muffin-cupcake pan with paper liners. Set aside.
In a large bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate medium size bowl, combine sugar, eggs, oil, vanilla extract, and mashed banana until well combined. Note: The batter will be lumpy from the bananas.
Add the dry ingredients to the mixing bowl with the wet and stir to mix until just combined. Stir in 2/3 cup chocolate chips, reserving a 1/3 cup for the tops.
Divide the batter evenly among muffin cups, filling them about 2/3 full. Sprinkle tops with reserved chocolate chips. (Depending on how the batter is divided, you may yield more. Have an extra pan handy.)
Bake the muffins for five minutes at 425°F degrees. Lower the oven temperature to 350°F. Bake for an additional 10-12 minutes, or until a toothpick comes out clean when inserted into the centers.
Cool in the pan for 5 minutes, then remove to a cooling rack to cool completely.
Store in an airtight container chilled or at room temperature for up to 2 days.