Preheat oven to 350 degrees F.
Bring a large saucepan of water to boil. Add the wild rice, cover partially and simmer over moderately low heat until tender (about 45 minutes). Drain well.
Add 2 tablespoons butter, chopped onion, garlic and celery to a medium saucepan, stirring occasionally until softened. Add jasmine rice and cook for 2 minutes. Add 2-1/2 cups water and 1 teaspoon salt. Bring to a boil. Cover and simmer over low heat until the water is absorbed and the rice tender (about 18 minutes). Fluff with a fork and transfer to a large bowl.
Cook sliced onion and remaining butter in a medium skillet until soft and golden. Then add to the jasmine rice mixture.
Brown sausage over moderate high heat; break it up as you cook it through. Stir in the chives, sage and thyme and scrape the mixture into the bowl. Add the chestnuts and drained wild rice. Season with salt and pepper.
Add the chicken stock. Boil until the stock is reduced to 1-1/2 cups. Add cornstarch mixture to the reduced stock, stirring until thickened. Stir stock into the rice stuffing and spread the stuffing in a buttered shallow 9x13 baking dish. Cover with foil and bake 30 minutes. Serve hot.