Preheat the oven to 350°F. Line two baking sheets with parchment paper or Silpat baking mats.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, sugar and light brown sugar until light and fluffy, about 2 minutes.
Add the eggs, one at a time, beating between each addition, then add the peanut butter, vanilla extract, baking soda and salt, mixing until combined. Add the oats and chocolate chips and mix just until combined.
Scoop 2-tablespoon mounds of the dough onto the lined baking sheets, spacing the cookies about 2 inches apart. Bake the cookies for 8 to 12 minutes. Remove the cookies from the oven and let them cool for 5 minutes on the baking sheets before transferring them to a rack to cool completely.