Pre-heat the oven to 350° F. Line an 8x8 pan with parchment paper.
In a large mixing bowl, using an electric mixer, combine the butter, brown sugar, and granulated sugar. Add the flour, egg, peanut butter, baking soda, vanilla, and salt to the mixing bowl. Mix until well combined. Stir in the oatmeal and chocolate chips.
Spread evenly in your pan (top with additional chocolate chips as desired for looks - and, chocolate!). Bake for 16-20 minutes until edges begin to brown. It's ok if the middle seems a bit underdone, they're like cookies in that you don't want them overbaked. They should be slightly gooey and will continue to set up as they cool.
Let cool slightly before serving; the longer you let them cool, the more set up the bars will be. However they're just so so good when enjoyed warm that I often will eat them warm with a fork. The bars are excellent served with ice cream or on their own. Store any leftovers covered at room temperature.
I like to use milk chocolate chips in these bars, however, semi-sweet or a combination of the two are just as delicious!You can use a 9x9 pan, the bars just won't be quite as thick. Reduce baking time slightly if doing so.