Preheat oven to 350°F. Line two large baking sheets with parchment paper or silicone baking mats and set aside.
In a large mixing bowl, whisk together the flour, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using an electric mixer, cream together the butter, brown sugar, and granulated sugar for about 1-2 minutes or until well combined. Mix in the peanut butter, egg, and vanilla extract until fully combined, making sure to stop and scrape down the sides of the bowl as needed.
Slowly mix in the dry ingredients until just combined, then mix in the oats. Add the chocolate chips and gently mix them into the cookie dough until well combined.
Using a 1.5 tablespoon cookie scoop, scoop balls of cookie dough onto the prepared baking sheets, making sure to leave a little room between each one. Roll the cookie dough into balls and very gently press down with your hand to flatten each ball of cookie dough slightly (make sure not to flatten them completely, just slightly).
Bake in separate batches at 350°F for 10-12 minutes or until the tops of the cookies are set. Remove from the oven and allow to cool on the baking sheet for 5-10 minutes, then transfer to a wire rack to finish cooling.