Into a large, re-sealable plastic bag add the soy sauce, sesame oil, peanut oil, lime juice, ginger, garlic, and cilantro. Seal the bag and shake it to mix the ingredients. Add the chicken breasts and shake it again. Let the chicken marinate in the refrigerator for at least 1/2 hour or up to overnight.
Pour about 1-inch of water into a wok and bring it to a boil over high heat. Line the bottom of a bamboo steamer with a layer of cabbage leaves. Place the marinated chicken on top of the leaves. Cover the steamer and put it into the wok. Steam the chicken until it is cooked through, about 10 to 15 minutes.