Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
In a large bowl, cream together butter, white sugar, and brown sugar until light and fluffy. Beat in egg, then stir in vanilla and peppermint extracts. Combine flour, cocoa powder, baking soda, and salt; gradually stir into the creamed mixture. Mix in the chocolate chips. Drop by rounded spoonfuls onto the prepared cookie sheets.
Bake for 12 to 15 minutes in the preheated oven. Allow cookies to cool on cookie sheets for 5 minutes before transferring to a wire rack to cool completely.