Combine root beer, apple cider vinegar, vegetable oil, soy sauce and salt and pepper in a large bowl or container to make marinade. Add chicken to marinade. Cover and refrigerate for at least 3 hours, or overnight.
Grill over medium-high heat until cooked through.
Notes
If you are concerned about the amount of sodium in the recipe, you could easily use lemon juice or a low sodium soy sauce. The chicken just needs something a little more acidic to make it tender and juicy for grilling.