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 ½ 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.