Preheat oven to 350F.
Whisk together flour, baking soda, and salt in a small bowl.
Beat the butter and sugars with a mixer at medium speed until pale and fluffy, about 3 minutes. Add the egg; beat until well blended. Add in the vanilla and peanut butter. Reduce the speed to low, beating until combined.
Gradually add the flour mixture, and beat until just combined. Stir in the cereal and chocolate chips.
Shape the dough into 1 ½-inch balls and place 1 inch apart on parchment-lined baknig sheets. Flatten the balls gently with a spatula or the tines of a fork.
Bake the cookies, rotating the baking sheets halfway through, until centers are firm and edgesare lightly browned, about 12 minutes. Transfer the cookies to a wire rack to cool completely.