Heat oil in a 12-inch skillet over medium-high heat until shimmering. Add the onions, garlic and tomato paste, and cook until the onions are softened and lightly browned, 8 to 10 minutes. Stir in the flour and cook for 1 minute. Slowly whisk in the wine and broth, scraping up any browned bits and smoothing out any lumps; transfer to a 6-quart slow cooker.
Add the thyme sprigs and bay leave to the slow cooker. Season the chicken with salt and pepper and place, breast-side-down, in the slow cooker. Cover and cook on low until the chicken is tender and registers 165 degrees F on an instant-read thermometer, 4 to 6 hours.
Transfer the chicken to a cutting board, tent loosely with aluminum foil, and let rest for 20 minutes. Let the liquid in the slow cooker settle for 5 minutes, then skim the fat off of the surface using a large spoon. Strain the liquid, discarding the solids, and season with salt and pepper to taste. Carve the chicken and serve with the sauce.