In a small bowl, whisk together the ingredients for the marinade until well combined.
Place the chicken breasts in a large resealable bag and pour the marinade over the top. Seal the bag and turn it over several times to coat the chicken evenly. Let the chicken marinate in the refrigerator for at least 30 minutes, or up to 4 hours.
Preheat the grill or a grill pan to medium-high heat. Remove the chicken from the marinade and discard the remaining marinade. Season the chicken with salt and pepper to taste.
Brush the grill or grill pan with olive oil, then add the chicken breasts and cook for 5-6 minutes per side, or until cooked through and no longer pink in the center.
Once the chicken is cooked, let it rest for a few minutes, then slice it into strips.
To assemble the rice bowls, divide the cooked rice evenly between four bowls. Top each bowl with sliced chicken, sliced avocado, chopped cilantro, and chopped red onion. Squeeze a lime wedge over each bowl before serving.
Serve the lime and cilantro chicken rice bowls immediately as a delicious and healthy meal. Enjoy!