Preheat the oven to 350 degrees F.
Put the vegetable oil and butter into a large skillet and place over high heat. Once the butter and oil are bubbling, add the chicken breasts to the skillet 4 at a time. Sear on each side until the chicken is golden, about 1 minute per side. Remove to a large baking dish. Repeat with the remaining breasts and set aside.
Add the onion and garlic and cook, stirring occasionally, until the onions are soft, about 5 minutes. Add the tomatoes, toss to combine and then follow with the balsamic vinegar and red wine and season with salt and pepper. Bring up to a bubble then reduce the heat and let simmer for 10 minutes. [Simmering the wine in this mixture does not reduce the alcohol content substantially.]
Pour the balsamic mixture over the chicken and place the pan in the top half of the oven for 10 minutes, or until the chicken has just cooked through. Remove from the oven, garnish with freshly chopped parsley and set into a prepared chafer.