Combine chicken breasts, olive oil, minced garlic, oregano, salt, and pepper in a large resealable bag.
Seal the bag and shake it well to coat the chicken evenly.
Marinate the chicken in the refrigerator for at least 30 minutes.
Preheat your grill to 350ºF (medium heat).
Place the marinated chicken on the grill and cook until it turns golden brown.
Check that it reaches an internal temperature of 165ºF.
While the chicken is grilling, slice the onions and mushrooms.
Heat a skillet over medium heat and add a little olive oil.
Sauté the onions and mushrooms together until they become tender and slightly browned.
Top each cooked chicken breast with sautéed onions and mushrooms.
Place a slice of Jack cheese over each piece of chicken.
Cover the chicken with a lid to allow the cheese to melt completely.
Serve immediately while hot.
Ensure you have a side dish ready to complement this delicious main course.