In a large bowl with an electric handheld mixer or in the bowl of a stand mixer, cream together the butter, peanut butter, brown sugar and granulated sugar. Add the vanilla and eggs and mix until the batter is light in color, 2-3 minutes. Stir in the flour, oatmeal, baking soda and salt. When it is mostly combined but there are still a few dry spots, add the chocolate chips and mix until well combined.
Scoop out tablespoon-sized balls of dough onto a lined baking sheet (with parchment, silpat or coated with cooking spray), spacing the cookies 1-2 inches apart. Bake for 10-12 minutes until very lightly browned and still soft in the center. Remove the cookies to a cooling rack to cool completely.