In a medium saucepan, combine the beets with enough salted water to cover by 3 inches. Add the sugar and simmer, covered, for 2030 minutes, or until tender when pierced with a knife. Drain the beets and remove the skin. In a blender, puree the beets with the chicken stock (you will need to do this in two batches). Set aside.
In a large saucepan, heat the butter over moderate heat. Add the onion and saute until soft, about 5 minutes. Add the garlic and rice, and saute another minute. Stir in the reserved beet puree and boil the mixture, stirring occasionally, for 10 minutes, or until thickened slightly. Reduce the heat to low, cover the pan, and simmer for 15 minutes, or until rice is tender and liquid is absorbed.
Sprinkle the chopped parsley over the rice and serve immediately.