Preheat oven to 350 degrees F (175 degrees C). Grease 2 baking sheets.
Beat butter, brown sugar, and white sugar together in a bowl with an electric mixer until creamy; beat in pudding mix. Add eggs and root beer concentrate; stir in flour and baking soda. Fold chocolate chips into the dough.
Drop spoonfuls of dough 2 inches apart on the baking sheets.
Bake in the preheated oven until golden, 8 to 10 minutes.