In a large bowl, mix butter with peanut butter (with hand mixer or stand mixer) until smooth. Add brown sugar and granulated sugar, and mix until creamy.
Beat in vanilla, egg, baking soda, and salt.
Mix in flour slowly until cookie dough forms. Stir in chocolate chips.
Scoop cookie dough balls (about 2 tablespoon sized) onto cookie sheets covered with parchment paper or silicone baking mats. Chill 30 minutes.
Preheat oven to 350°F.
Press cookie dough balls flat with the tines of a fork.
Bake cookies for 8-12 minutes, or until slightly brown on the bottom and the top just loses the wet cookie dough look.
Store in an airtight container for up to 3 days or freeze for up to 30 days.