Preheat oven to 425 degrees F. Brush the 1 tablespoon oil over bison tenderloin roast. For rub, stir together salt, thyme, and coarsely ground black pepper in a small bowl. Sprinkle mixture evenly over bison tenderloin; rub in with your fingers.
Place bison tenderloin on a rack set in a shallow roasting pan. Insert an oven-going meat thermometer into center of the bison tenderloin. Roast, uncovered, for 1 hour 10 minutes or until meat thermometer registers 135 degrees F for medium rare. (For medium, roast for 45 to 50 minutes or until meat thermometer registers 150 degrees F.)
Transfer bison tenderloin to a cutting board. Cover bison tenderloin with foil; let stand for 15 minutes. Temperature of the bison tenderloin after standing should be 145 degrees F to 160 degrees F.
Slice bison tenderloin across the grain and arrange on a serving platter. Serve with Cherry-Onion Chutney.
Cherry-Onion Chutney: Heat the 1 tablespoon oil over medium-high heat in a large skillet. Cook onions in hot oil for 8 to 10 minutes or until golden brown. Remove onions from skillet; set aside. Add brown sugar, vinegar, cinnamon, cloves and cayenne pepper to skillet. Bring to boiling; reduce heat. Add cherries. Simmer, uncovered, for 15 minutes. Add pears and cook for 5 more minutes or until pears are softened. Stir in cooked onion. Season to taste with salt and black pepper.