Combine all of the marinade ingredients in a large, nonreactive bowl or resealable plastic freezer bag. Add the chicken and turn to coat. Refrigerate overnight or for at least 2 hours.
Place chicken and marinade in a large lidded pot or Dutch oven over high heat and bring to a boil. Immediately reduce heat to a simmer and cook, stirring occasionally, until the chicken is cooked through and tender, around 30 minutes.
Heat broiler. Transfer chicken pieces to a large bowl, raise heat under the pot to medium-high, and reduce the sauce until it achieves almost the consistency of cream, about 10 minutes. Remove bay leaves and chilies.
Place chicken pieces on a roasting pan and place under broiler for 5 to 7 minutes, until they begin to caramelize. Remove, turn chicken, baste with sauce and repeat, 3 to 5 minutes more. Return chicken to sauce and cook for a few minutes more, then place on a platter and drizzle heavily with sauce.