Arrange chicken breasts in a baking dish; add tequila and juice of 1/2 a lime. Sprinkle 1/2 of the lime zest, 1/2 of the garlic powder, and 1/2 of the chili powder over the chicken. Cover dish with plastic wrap and marinate in the refrigerator for 30 minutes.
Turn chicken breasts; sprinkle remaining lime juice, lime zest, garlic powder, and chili powder on top. Cover again and marinate in the refrigerator for another 30 minutes.
Preheat the oven to 425 degrees F (220 degrees C). Uncover baking dish and discard tequila-lime marinade.
Bake chicken in the preheated oven for 25 minutes. Sprinkle Mexican-style cheese over the chicken and continue to bake until the chicken is no longer pink in the center and the juices run clear, about 10 minutes more. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).