Slice open the limes and squeeze the juice into a food processor or blender. Add the tequila, olive oil, salt, garlic, jalapenos and cilantro. Blend the mixture until totally combined. Add the chicken to a large plastic bag and pour in the lime-tequila mixture. Seal the bag and marinate in the fridge for several hours or overnight.
Remove the chicken from the bag and grill it over medium-high heat. Rotate the chicken 45-degrees on both sides to create nice grill marks, and continue grilling until the chicken is cooked through, 4 to 5 minutes per side.
Melt the Monterey Jack over the top of the sliced chicken breasts.
Slice the chicken and serve it on a plate topped with the sides.