Preheat oven to 350°F (175°C). Line baking sheets with silicone liners or parchment paper.
Whisk together the flour, oats, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, brown sugar, and sugar until light and creamy. Add the peanut butter, and mix until combined. Add the eggs and vanilla, and mix until combined.
Reduce mixer speed to low. Gradually add the flour mixture, mixing just until combined. Stir in the chocolate chips.
Drop the dough by 2-tablespoon portions onto the prepared pans. Bake 10 to 12 minutes, or until the cookies are lightly browned but the centers are still soft. (Place the cookie dough in refrigerator between baking batches.)
Cool the cookies on pan for 5 minutes. Then, transfer the cookies to wire racks to cool completely.
Notes
*Either kind of peanut butter will work, so just go with your preference. Use a regular shelf-stable peanut butter (like Jif or Skippy).
Recipe slightly adapted from MyRecipes.
How to store: You can keep these cookies in an airtight container at room temperature for 4 to 5 days, or freeze them for up to 3 months.