Arrange fennel and onions in the bottom of a roasting pan or heavy cast iron skillet. Rinse chicken with cold water, pat dry and set in the middle of the pan.
Season inside cavities and outside of the chicken liberally with salt and pepper. Place thyme springs on top of vegetables and drizzle everything with olive oil.
Roast uncovered for about 1 hour or until internal temperature reaches 165°F. Sprinkle chestnuts in roasting pan for last 15 minutes of roasting to heat.
While chicken is roasting, bring a large pot of water to a boil. Add yams and simmer until tender, about 15 to 20 minutes. Drain well and return to pot. Mash with a potato masher or fork and stir in orange juice and vegan butter or coconut oil.