Place the chicken in a 6-quart pot. Pour the water, vinegar, and soy sauce over the chicken. Add the sugar, onion, garlic, peppercorns, and bay leaves to the pot; bring the mixture to a boil for 2 minutes. Reduce heat to low; simmer until the chicken is no longer pink at the bone and the juices run clear, about 30 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 180 degrees F (82 degrees C). Remove the chicken from the pot and continue cooking the sauce until it thickens, about 10 minutes; season with salt.
Return the chicken to the pot, making sure the chicken is covered entirely by the sauce. Cook together until the chicken is reheated, about 3 minutes.