In a large bowl, cream together the butter, brown sugar and white sugar until light and fluffy. Beat in the egg, then stir in the vanilla. Combine the flour, baking soda and salt; gradually stir into the creamed mixture. Finally, stir in the chocolate and peanut butter chips. Drop by rounded spoonfuls onto the unprepared cookie sheet.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.