1. Rinse thighs and pat dry. Pull off and discard skin; trim off and discard lumps of fat. Sprinkle thighs lightly with salt and pepper.
2. Place thighs in a 4 1/2-quart or larger electric slow-cooker. Sprinkle with garlic and chopped rosemary; pour wine and broth over chicken.
3. Cover and cook until meat pulls easily from the bone, about 5 hours on low, 3 hours on high.
4. Skim and discard fat from juices. Add rice and mix to moisten evenly. Turn cooker to high; cover and cook, stirring several times, until rice is just tender to bite, about 5 minutes. Spoon chicken and rice onto a platter. Sprinkle with onions and garnish with rosemary sprigs. Add salt and pepper to taste.