Combine lime juice, garlic cloves, sliced jalapeno, salt, cilantro, and tequila in a food processor or blender. Pulse until combined. Turn on the blender/food processor and drizzle in the olive oil until it’s all combined.
Slightly flatten chicken breasts with a mallet or the bottom of a heavy skillet. Place in a plastic bag and pour in marinade. Seal bag and marinate for several hours or overnight.
When ready to cook, remove chicken from bag and place on the grill. Cook until completely done. Toward the end of cooking, top chicken breasts with grated Monterey Jack and allow to melt. (You can also top chicken with cheese and melt under the broiler.)
Serve topped with Pico de Gallo or salsa, alongside refried black beans, our Mexican Rice, sour cream, avocado slices and fresh flour tortillas.