Trim fat from meat. If needed cut meat to fit into a 3.5-4 quart slow cooker. Sprinkle the meat with the salt and pepper. In a large skillet brown meat on all sides in hot oil. Drain off fat. Transfer meat to cooker. Add onions, the 1 cup root beer, and the garlic.
Cover and cook on low-heat setting for 8-10 hours or on high heat for 4-5 hours.
For sauce, in a medium saucepan stir together the 3 cups root beer and the chili sauce, Bring to boiling, reduce heat. Simmer, uncovered about 30 minutes or until mixture is reduced to 2 cups, stirring occasionally,
Transfer meat to a cutting board. Using two forks, pull meat apart into shreds, place on platter. Transfer onions to plater. Discard cooking liquid. Drizzle meat with root beer sauce.