1. In a 3- to 4-quart pan, combine the garlic, onion, and salad oil. Cook, stirring often, over medium-high heat until the onion is lightly browned, about 5 minutes.
2. While the onion cooks, cut the chicken into bite-size pieces. When the onion has browned, add the chicken pieces, red chili sauce, oregano, and chicken broth. Bring to a boil, reduce heat, and simmer until chicken is no longer pink in center of thickest part (cut to test), 7 to 8 minutes.
3. Add hominy, reheat to simmering, and serve. Offer lettuce and lime wedges to add to taste.