Heat a large Dutch oven over medium heat, add 2 tablespoons of the olive oil. Season the chicken parts with salt and pepper. Working in batches, fry the chicken until golden brown, about 7 minutes per side. Set the browned chicken aside on a platter. Discard the oil.
Return the Dutch oven to the heat and add the remaining oil. Saute the pancetta until golden brown, about 5 to 7 minutes. Remove the pancetta with a slotted spoon and reserve. Add the onion, carrot, and celery and scrape up the browned bits with a wooden spoon. Reduce the heat to medium-low and cook, stirring occasionally, until the vegetables are golden brown, about 15 to 20 minutes. Add the garlic and marjoram or oregano and cook for 2 minutes more. Add the wine and cook over high heat, stirring frequently, until the liquid is reduced by about two thirds. Add the reserved pancetta, tomatoes, and puree; season with salt and pepper to taste. Bring the sauce to a slow simmer and partially cover. Cook, stirring occasionally, until the flavors come together, about 35 to 40 minutes.
Preheat the oven to 350 degrees F. Add the chicken pieces to the simmering sauce and cook for 1 minute to heat through. Transfer the pan to the oven, and cook the chicken until tender, about 35 to 40 minutes.
Remove the chicken from the oven and transfer the meat to a heated platter, and cover loosely with foil. With a large spoon or ladle, skim any fat off the surface of the sauce and discard. Stir the parsley into the sauce, and season with salt and pepper to taste. Pour the sauce over the chicken and serve.
