Preheat the oven to 350ºF. Line a large baking sheet with parchment paper or a silpat.
In the bowl of a stand mixer fitted with a paddle attachment, cream together butter and sugars on medium speed until light and fluffy. Beat in the bananas, eggs and vanilla. Gradually add the flour and baking soda and mix on low until well blended. Add oats and chocolate chips and mix just until incorporated.
Drop batter by the spoonful onto the prepared baking sheet, leaving about 2 inches between cookies. Bake for 15 minutes or until golden brown. Let cool slightly on the pan before removing to a rack to cool completely.