Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 10x15 inch jelly roll pan.
In a large bowl, cream butter, white sugar and brown sugar until fluffy. Beat in egg and vanilla. Fold in mashed banana. In a separate bowl, mix flour, baking powder and salt. Fold flour mixture into butter mixture. Stir in chocolate chips. Spread in prepared pan.
Bake in preheated oven 20 minutes, until set. Cool before cutting into squares.