Preheat the oven to 350 degrees F. Lightly spray a 9-by-13-inch glass baking dish with nonstick cooking spray.
Combine the butter, brown sugar and granulated sugar in a large bowl and beat using a handheld mixer until light and fluffy, about 2 minutes. Add the peanut butter, vanilla extract and eggs and beat again until fully combined. Add the flour, baking soda and salt and mix on low speed until the mixture is just fully mixed. Fold in the oats and chocolate chips with a rubber spatula. Spread the mixture in the prepared baking dish and bake until just set, 30 to 35 minutes. Do not over bake. Allow to cool completely before cutting into squares and serving.