Quarter limes and juice into a food processer or blender
Add the balsamic vinegar, olive oil, salt, garlic, jalapenos and cilantro
Blend mixture until totally combined
Add the chicken to a large plastic bag and pour the lime mixture over the chicken and marinate for several hours or overnight
When ready, remove chicken from the marinade and grill on medium-high heat
Rotate chicken 45 degrees on both sides to create nice grill marks and continue grilling until the chicken is cooked through, about 4-5 minutes per side
Place the shredded Monterey Jack cheese over the warm chicken breasts to melt
Slice the chicken and serve on a place with any number of side dishes
Optional serving additions: Corn or flour tortillas, corn chips, salsa, Jalapeno slices, lime wedges, avocado slices, sour cream, spicy rice