Prepare the grill for direct grilling over medium-high heat.
In a 9-inch square baking pan, stir together the vegetable oil, lime juice, chopped green chilies, and chopped garlic to make the marinade.
Add the chicken breasts to the marinade, ensuring they are fully coated.
Marinate in the refrigerator for at least 45 minutes, turning once halfway through.
Remove the chicken from the marinade and allow any excess marinade to drain off.
Grill the chicken over hot coals for about 7 minutes on each side or until the chicken is fork-tender and cooked through.
Once the chicken is almost cooked, top each piece with 2 slices of Cheddar cheese and continue grilling until the cheese begins to melt.
Remove the chicken from the grill and serve hot with salsa on the side.
Notes / Tips / Wine Advice:
Serving Tip:Serve with warm tortillas, sautéed peppers and onions, and your favorite toppings for a complete fajita experience.Wine Advice:Pair these flavorful Grilled Fajita-Style Chicken Breasts with a light-bodied red wine such as Merlot or a crisp, dry white wine like Sauvignon Blanc to complement the bold flavors of the dish and refresh the palate.