Preheat the oven to 350°F.
In a large Dutch oven, cook the bacon over medium heat until crispy. Using a slotted spoon, transfer the bacon to a plate and set aside.
Season the chicken thighs with salt and pepper, then add them to the Dutch oven skin-side down. Cook until golden brown, about 5-7 minutes per side. Transfer the chicken to a plate and set aside.
Add the onion, garlic, carrots, and celery to the Dutch oven and cook until the vegetables are softened, about 5-7 minutes.
Add the flour and tomato paste, stirring constantly, until the vegetables are coated and the flour is lightly browned.
Pour in the red wine and chicken broth, stirring to combine. Add the thyme leaves and bay leaf, then bring to a simmer.
Return the chicken and bacon to the Dutch oven. Cover with a lid and transfer to the oven.
Bake for 1 1/2 to 2 hours, or until the chicken is tender and falling off the bone.
Remove the Dutch oven from the oven and stir in the butter until melted and incorporated.
Serve hot, garnished with chopped fresh parsley.