Sprinkle roast evenly with 1 teaspoon salt and 1/2 teaspoon pepper.
Brown roast on all sides in hot oil in a large ovenproof Dutch oven over medium-high heat. Add onion. Remove Dutch oven from heat.
Stir together remaining 1/2 teaspoon salt, remaining 1/2 teaspoon pepper, root beer, chili sauce, and garlic until blended. Pour root beer mixture over roast mixture in Dutch oven.
Bake, covered, at 300° for 3 hours or until tender.