Preheat oven to 350 degrees F. Lightly grease a 9×13-inch baking pan.
Beat butter, brown sugar, and white sugar in a bowl until creamy; beat in eggs until smooth. Stir pudding mix into creamed mixture, followed by vanilla extract. Whisk flour, baking soda, and salt together in a separate bowl and stir flour mixture into moist ingredients. Mix oats and chocolate chips into dough. Press dough into prepared baking pan.
Bake in the preheated oven until lightly browned, about 25 minutes. Let cool before cutting into squares.