Combine sugar in a medium mixing bowl. Cut in shortening with a pastry blender.
Sift together flour, soda, and salt in a small mixing bowl; add to sugar mixture, mixing well. Add egg and vanilla, stirring well. Stir in chocolate morsels.
Drop by teaspoonfuls 2 inches apart onto greased and floured cookie sheets. Bake at 350° for 8 to 10 minutes. Cool slightly on cookie sheets. Remove to wire racks to cool completely.