In a large bowl, using a hand-held mixer or stand mixer with paddle attachment, cream the butter and sugars together on medium speed. Beat in the peanut butter, egg, and vanilla (in that order). Beat in the baking soda and flour. Do not over mix. Fold in the chocolate chips. Cover the dough tightly and chill in the refrigerator for at least 30 minutes.
Preheat oven to 350F degrees. Line a large baking sheet with parchment paper or a silicone mat. Scoop 1 Tablespoon of dough and roll into a ball. Press down to slightly flatten them out. Bake for 8-9 minutes. Cookies will be soft and may appear undone. They will firm up as they cool. Allow to cool completely on a wire rack.
Store cookies in a airtight container at room temperature for 10 days.