Heat olive oil over medium-high heat.
Season both sides of chicken with salt and pepper.
Brown chicken for about 3 minutes on each side.
Add chicken, onions, peppers, carrots, and mushrooms to crock-pot.
Mix tomatoes, garlic, oregano, and red wine vinegar together.
Pour tomato mixture over chicken, and vegetables and stir slightly to allow tomato mixture to coat vegetables and chicken.
Cook on low for 6-8 hours or high for 4-5 hours.
To thicken the tomato sauce, remove chicken to a serving platter and keep warm.
Mix together corn starch and water and then stir into sauce remaining in the crock-pot.
Cook on high for 15 minutes.
Return chicken to crock-pot or pour sauce over chicken on serving platter.