Beat white sugar and brown sugar together in a large bowl using an electric mixer until smooth and fluffy; beat in peanut butter until smooth. Beat eggs and vanilla extract into sugar mixture until creamy. Mix flour and baking soda into sugar mixture until dough is just mixed; fold in chocolate chips. Form dough into ping pong ball-size balls and arrange on a baking sheet.
Bake in the preheated oven until cookies are golden brown, about 20 minutes. Cool cookies on the baking sheet for 10 minutes.