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 egg, peanut butter, vanilla extract, flour, baking soda, and salt until just combined. Stir in the oatmeal and chocolate chips.
Spread the dough evenly in your pan. Top with additional chocolate chips as desired for looks - and, chocolate! Bake for 18-22 minutes until edges are set and begin to just turn golden brown. The middle will be slightly jiggly, but that's what you want. The bars are like cookies in that you don't want them overbaked, with a slightly gooey center. If you prefer them more well done, bake for an additional 5-7 minutes.
Place the pan on a cooling rack and let it cool at least 15-20 minutes before serving so they have time to set up. The longer you let them cool, the more set they will be. However, they're just so so good when enjoyed warm that I often will eat them warm with a fork instead of "bar form".
The bars are excellent served with ice cream or on their own. Store any leftovers covered at room temperature.