01 - In a medium bowl, combine the Coca-Cola, ketchup, soy sauce, apple cider vinegar, brown sugar, minced garlic, smoked paprika, black pepper, and salt. Whisk until thoroughly blended and the sugar has dissolved.
02 - Place the chicken breasts in a large resealable plastic bag or a shallow dish. Reserve 1/2 cup of the glaze mixture and set aside for basting later. Pour the remaining marinade over the chicken, seal the bag or cover the dish, and refrigerate for at least 1 hour or up to 8 hours for deeper flavor.
03 - Preheat your grill to medium-high heat, approximately 375°F to 400°F. Lightly oil the grill grates using a folded paper towel dipped in vegetable oil to prevent the chicken from sticking.
04 - Remove the chicken from the marinade and discard the used marinade. Place the chicken breasts on the grill, close the lid, and cook for 5 to 6 minutes per side. Baste occasionally with the reserved Coca-Cola glaze during grilling. Cook until the internal temperature of the thickest part reaches 165°F as measured with a meat thermometer.
05 - Transfer the grilled chicken to a cutting board and let it rest for 5 minutes to allow the juices to redistribute. Garnish with chopped fresh parsley if desired, and serve warm.