Preheat oven to 375 degrees F (190 degrees C). Grease a 9x13 baking dish.
Bring the rice and water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until rice is tender and the liquid has been absorbed, 20 to 25 minutes. Allow rice to cool slightly.
Meanwhile, bring a large pot of water to a boil. Remove the core from the cabbage, and place cabbage in the boiling water. Remove the outer leaves as they soften. Set leaves aside.
Heat butter in a skillet over medium heat, and cook and stir the onion until softened and translucent, about 5 minutes. Stir together the cooked onion, ground chicken, cooked rice, eggs, garlic, salt, pepper, and marjoram in a bowl.
Place about 1/4 cup of the meat mixture in the center of each cabbage leaf. Roll leaf and tuck ends in to enclose filling. Secure each roll with a toothpick if necessary. Place rolls into prepared baking dish. Pour tomato sauce over the rolls.
Bake, covered, in the preheated oven until the meat in the rolls is no longer pink, 45 to 60 minutes. An instant-read thermometer inserted into the center of casserole should read at least 160 degrees F (70 degrees C).