Combine apple cider vinegar, onion, ginger, lemon peel, orange peel, cinnamon stick pieces, crushed red pepper, and ground cloves in heavy large saucepan. Boil mixture until reduced to 1 1/2 cups, about 10 minutes. Add cranberries, brown sugar, and pears; stir over medium heat until sugar dissolves. Reduce heat to medium-low; cover and simmer until pears are very tender, berries collapse, and flavors blend, stirring occasionally, about 30 minutes. Remove from heat; discard cinnamon stick pieces. Using potato masher, mash mixture coarsely. Transfer chutney to bowl and cool. MAKE AHEAD: Can be made 3 days ahead. Cover and chill. Bring to room temperature before serving.