Sprinkle salt and pepper all over chicken. Warm oil in a large skillet over medium-high heat. Brown chicken on both sides (in batches, if necessary), 3 to 4 minutes per side. Transfer chicken to a slow cooker. Discard all but 1 Tbsp. fat from skillet.
Add mushrooms, onions and rosemary to skillet and cook, stirring occasionally, for 4 minutes. Add garlic and cook, stirring, 2 to 3 minutes longer, until mushrooms have released their juices and onions have softened and are translucent.
Pour wine into skillet and cook, scraping up any browned bits with a wooden spoon. Cook, stirring occasionally, until wine is slightly reduced, 2 to 3 minutes. Stir tomatoes into mushroom mixture and bring to a simmer.
Pour wine mixture over chicken in slow cooker, cover and cook on low heat until chicken is tender and juices run clear when pierced in the thickest part with a knife, about 4 hours.
Skim and discard any grease from surface. Remove chicken from pot and arrange on a platter. Spoon sauce over chicken.