Combine the pear and lemon juice; set aside. Place water in a medium skillet, and bring to a boil. Stir in 3 tablespoons sugar, cinnamon, and cloves; reduce heat to medium. Add pear mixture; cover and cook 6 minutes or until tender. Remove pear with a slotted spoon, and keep warm. Add honey to pan, and cook until mixture begins to thicken (about 5 minutes).
Combine the chestnuts and 2 tablespoons sugar in a small saucepan over medium heat; cook 3 minutes or until sugar coats the chestnuts, stirring frequently. Remove chestnuts from pan. Cool on wax paper. Arrange pear on 2 serving plates. Pour sauce over pear, and top with frozen yogurt. Sprinkle with chestnuts, and serve immediately.