In a large saucepan, bring the sugar, water and red-hots to a boil. Cook and stir until red-hots are dissolved, about 5 minutes. Reduce heat; carefully add apples. Cover and simmer for 15 minutes or just until apples are tender, turning once.
With a slotted spoon, remove apples to a large bowl. Bring syrup to a boil; cook, uncovered, until reduced to about 1-1/2 cups. Cool. Pour syrup over apples; cover and refrigerate until serving.