In a large bowl, cream butter and shortening; gradually add sugars, beating well at medium speed with an electric mixer. Beat in egg and vanilla. Combine flour, soda, and salt; stir into creamed mixture. Stir in chocolate chips. Chill dough for 1 hour.
Preheat oven to 350 degrees F (175 degrees C). Lightly grease cookie sheets. Drop dough by heaping tablespoonfuls 3 inches apart onto prepared cookie sheets.
Bake for 12 to 14 minutes in preheated oven. Cookies will be soft. Cool slightly on cookie sheets; transfer to wire racks to cool completely.