In a large saucepan, cook rice according to package directions.
Meanwhile, preheat the broiler. Broil chiles, skin side up, as close to the heat as possible, until skin blisters and begins to blacken, about 5 minutes. Remove from broiler and place in sealable plastic bag; close bag and let stand 10 minutes. Peel chiles, then cut into thin strips.
Season both sides of chicken cutlets with salt and black pepper to taste. In a large, nonstick skillet, heat olive oil over medium heat. Add chicken and lightly brown all over, 2 to 3 minutes per side. Don't overcook. To check doneness, make sure juices run clear when chicken is pierced. Remove chicken from skillet and cover to keep warm.
In the same skillet, sauté onion until soft, about 5 minutes. Add chile strips. Add Mexican crema and stir until heated. Season with salt and black pepper to taste.
When rice is done and all liquid is absorbed, remove from heat and stir in cilantro and parsley. Pour sauce over chicken and serve with rice.