Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, use an electric mixer to cream together the peanut butter, softened butter, granulated sugar, and brown sugar until smooth and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the peanut butter mixture and beat until fully incorporated.
In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Stir in the rolled oats and chocolate chips with a spatula until evenly distributed.
Using a tablespoon or cookie scoop, drop rounded spoonfuls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden but the centers are still soft.
Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.