Marinate the Chicken: In a bowl, combine the bouillon, lime juice, honey, cilantro, garlic, soy sauce, chili lime seasoning, onion powder, paprika, salt, and pepper. Reserve 1 tablespoon of the marinade for brushing while cooking. Set aside. Add the chicken and toss to coat.
Cook the Rice: Rinse the basmati rice under cold water. In a saucepan, bring the water to a boil. Add the rice, bay leaf, and salt. Stir once, cover, and reduce heat to low. Simmer until water is absorbed, about 18 minutes for white rice or about 50 minutes for brown rice. Remove from heat and let steam, covered, for 5 minutes. Remove bay leaf, fluff with a fork, then stir in olive oil, lime juice, lemon juice, and cilantro.
Cook the Chicken: Heat a skillet over medium heat. Add the marinated chicken and cook until golden and cooked through, brushing with reserved marinade if desired for extra glaze.
Serve: Spoon cilantro lime rice into bowls and top with honey lime chicken. Spoon any extra pan juices over the top before serving.