Preheat oven to 375°F. Combine thyme, salt and pepper in a small bowl.
Remove giblets (if included) from game hens and trim any excess skin. Loosen the skin over the breast and thigh meat and rub half the thyme mixture under the skin. Tie legs together with kitchen string.
Heat butter and oil in a large roasting pan set over 2 burners on medium heat. Add the game hens and brown on all sides, turning occasionally, 10 to 12 minutes.
Add onion to the pan, transfer to the oven and roast for 10 minutes. Add Brussels sprouts and roast for 20 minutes. Stir chestnuts and the remaining thyme mixture into the pan. Continue roasting until an instant-read thermometer inserted into a thigh registers 165°F, 10 to 15 minutes more.
Transfer the game hens to a large cutting board and let rest for 10 minutes. Place the roasting pan over 2 burners on medium heat. Toss the vegetables with vinegar and bring to a simmer, gently stirring and scraping up any browned bits. Remove the string from the game hens, turn breast-side down and slice in half lengthwise using a large heavy knife, cutting straight through to the breast side. Serve the game hens with the vegetables.
Per serving :
7 g Fat;
2 g Sat;
2 g Mono;
93 mg Cholesterol;
39 g Carbohydrates;
24 g Protein;
6 g Fiber;
656 mg Sodium;
875 mg Potassium
2 Carbohydrate Serving
Exchanges: 2 starch, 1 vegetable, 3 lean meat
Tips & Notes
Make Ahead Tip: Equipment: Kitchen string
Shopping tip: Cooked peeled chestnuts are available in jars in the baking aisle or with seasonal foods at many supermarkets.