HEAT oven to 350°F.
BEAT butter and 1 cup sugar in large bowl with mixer until light and fluffy. Add flour and cornstarch; mix well. Stir in chocolate.
ROLL dough into 1-inch balls; place, 3 inches apart, on baking sheets. Flatten slightly with bottom of glass.
BAKE 13 min. or until centres are set and tops are lightly browned; cool on baking sheets 5 min. Add warm cookies, 1 at a time, to remaining sugar, turning to evenly coat both sides of each. Cool completely on wire racks.