Grease a cookie sheet. Set cookie sheet aside. In a medium mixing bowl beat egg whites and vanilla with an electric mixer on medium speed until soft peaks form ( tips curl). Gradually add sugar, 1 tablespoon at a time, beating on high speed about 7 minutes or until very stiff peaks form ( tips stand straight) and sugar is almost dissolved. Fold in coconut.Drop coconut mixture from a rounded teaspoon 2 inches apart on the prepared cookie sheet. Bake in a 325F oven for 15 to 20 minutes or until edges are lightly browned. Remove cookies from cookie sheet and cool on a wire rack.