1Season the chicken with salt and pepper.
In a large skillet with a lid, heat the oil and 1 tablespoon of the butter over medium-high heat.
When the oil and butter are hot,(not smoking), brown the chicken in batches until the skin turns , golden brown. Turn over and brown the other side. Each side should take about 5 minutes.
When all the chicken has been browned, remove it and carefully pour out the cooking fat.
Return the chicken to the skillet and very slowly add the red wine vinegar. The fumes can be quite intense. Reduce vinegar by about half, turning chicken periodically to coat it, about 10 minutes.
Add tomatoes and chicken stock, cover and simmer gently over medium-low heat until the flavors have mingled and the chicken is cooked through, about 20 minutes.
2If making the dish ahead of time, as recommended for maximum flavor, stop at this point.
Remove chicken from sauce and keep warm. If re-heating, heat the chicken through in the sauce then remove to a warmed dish while you finish the sauce.
Remove pan from heat and whisk in the remaining 3 tablespoons butter, creating a rich, glossy sauce. Season to taste with salt and pepper.
Pour over the chicken and sprinkle with the parsley.