Light coat the inside of the slow cooker insert with vegetable oil.Turn the slow cooker on high to preheat while you prepare the ingredients.
In a small microwave safe bowl combine the olive oil, tomato paste,garlic, thyme and pepper flakes. Stir to mix and microwave in 10 second intervals until fragrant, about 30 seconds.
Transfer the oil mixture to the bottom of the slow cooker, Stir in the broth, balsamic, black pepper, and cornstarch.
Season the chicken with salt and pepper and transfer to the slow cooker. Cover and cook on low for 3 hours 30 minutes.
Add the tomatoes and arrange them under the chicken and continue cooking for 20 minutes.