2 tbsp. white-wine vinegar
16 oz. jarred roasted chestnuts, (2½ cups; see Shopping Tip)
2 pounds Brussels sprouts, trimmed and cut in half if large (about 6 cups)
1 large red onion, peeled and cut through the root end into 8 wedges
2 tsp. extra-virgin olive oil
2 tsp. butter
4 Cornish game hens, 1-1½ pounds each
1 tsp. freshly ground pepper
2 tsp. salt
1 tbsp. chopped fresh thyme