Preheat oven to 375 degrees F (190 degrees C). Lightly grease 2 large cookie sheets with vegetable shortening.
Cream the butter and sugars together in a large bowl. Beat in the egg and vanilla extract until well blended. Sift together the flour, baking soda, and salt; gradually blend into the batter. Stir in the chopped macadamia nuts and chocolate chips. Drop by rounded teaspoonfuls onto the cookie sheets, about 2 inches apart.
Bake in preheated oven for 10 to 12 minutes, or until the cookies are golden brown. Remove from the oven, and transfer the cookies to cooling racks.