Preheat the oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking dish.

Bring 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 onion until softened and translucent, about 5 minutes. Stir together cooked onion, ground chicken, cooked rice, eggs, garlic, salt, pepper, and marjoram in a bowl.

Place some 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 the prepared baking dish. Pour tomato sauce over the rolls.