In a medium bowl, whisk together 2 cups Dr. Pepper, 1/3 cup soy sauce, 1 tablespoon minced garlic, 1/2 cup brown sugar, 1 tablespoon balsamic vinegar, and 1 tablespoon lime juice until the sugar is dissolved and the marinade is uniform.
Place 6 chicken breasts in a large gallon-sized zipper bag or a nonreactive container and pour the marinade over the chicken, ensuring all pieces are coated.
Seal the bag tightly and refrigerate for 4 to 24 hours to marinate.
When ready to cook, remove the chicken from the marinade and discard the marinade.
Preheat your grill or a cast iron grill pan to medium-high heat. Grill the chicken until it reaches an internal temperature of 165ºF (74ºC), flipping as needed for even cooking.
Use a meat thermometer to confirm doneness, then remove the chicken and let it rest a few minutes before serving.