Step 1

In a blender, combine the vinegar, ketchup, soy sauce, sugar, garlic, bay, peppercorns and 1½ teaspoons salt. Blend until well combined and the bay leaves are broken into tiny bits, 15 to 30 seconds. Pour the mixture into a large bowl, then stir in the soda.

Step 2

If using chicken breasts, use a sharp chef's knife to cut each in half crosswise. Cut 2 or 3 diagonal slashes about ½ inch deep through the skin and meat of each piece of chicken. Add the chicken to the marinade and turn to coat. Cover and refrigerate for 1 hour or up to 2 hours.

Step 3

Prepare a charcoal or gas grill for indirect cooking. For a charcoal grill, spread a large chimney of hot coals evenly over one side of the grill bed; open the bottom grill vents and the lid vent. Heat the grill, covered, for 5 to 10 minutes, then clean and oil the grate. For a gas grill, turn all burners to high and heat, covered, for 15 minutes, then clean and oil the cooking grate; leave the primary burner on high and turn the remaining burner(s) to low.

Step 4

While the grill heats, transfer the chicken to a large plate, allowing the marinade to drip off. Pour the marinade into a medium saucepan, bring to a simmer over medium and cook, stirring occasionally, until reduced to 1 cup, about 20 minutes. Stir in the lime juice and set aside. Set aside ⅓ cup for serving; use the remainder as a basting sauce.

Step 5

Place the chicken skin side up on the cooler side of the grill. Cover and cook for 15 minutes. Generously brush the pieces with basting sauce, then re-cover and cook until the thickest part of the breast, if using, reaches 160°F or the thickest part of the thighs and drumsticks, if using, reach 175°F, another 15 to 20 minutes.

Step 6

Brush the chicken with the reduced sauce, thenflip the chicken skin side down onto the hot side of the grill. Cook until deeply browned, about 1 minute. Brush the bone side with basting sauce, then flip a final time and cook until deeply browned, about 1 minute. Transfer skin side up to a platter and let rest for about 5 minutes. Serve with the reserved sauce.