Heat the vegetable oil in a large skillet over medium-high heat. Cook chicken pieces until golden brown on both sides, then remove. Stir in the onion and garlic; cook until they soften and brown, about 6 minutes.
Pour in vinegar and soy sauce, and season with garlic powder, black pepper, and bay leaf. Add the browned chicken, increase the heat to high, and bring to a boil. Reduce heat to medium-low, cover, and simmer until the chicken is tender and cooked through, 35 to 40 minutes.