Position a rack in the center of the oven and heat the oven to 350ºF.
Put the anchovies, garlic, and chopped rosemary in a food processor and process until finely chopped, scraping the sides of the bowl as needed. Add the chicken broth and process again until the ingredients are well blended, about 30 seconds.
Season the chicken pieces generously with salt and pepper. In a straight-sided 10- or 11-inch ovenproof sauté pan with a lid, heat the oil over medium-high heat until very hot. Arrange the chicken pieces skin side down in the pan (it’ll be crowded), cover with a splatter screen, if you have one, and cook until deeply browned, about 5 minutes. Turn the pieces over and cook until the other sides are deeply browned, 3 to 5 minutes more. Transfer to a plate. Pour out and discard all the fat from the pan.
Return the pan to medium-high heat, carefully add the wine to the pan, and bring to a boil, scraping the browned bits from the bottom of the pan with a wooden spoon. Pour in the broth mixture. Return the chicken pieces to the pan, along with any accumulated juices. Add the tomatoes and cover. Transfer the pan to the oven and braise until the chicken is fork-tender and the drumstick meat starts to come away from the bone, 45 to 50 minutes.
With a slotted spoon, transfer the chicken and tomato pieces to a large serving dish and keep warm by covering the dish loosely with foil. Tilt the sauté pan and skim off as much fat as possible from the sauce. Bring the sauce to a boil over medium-high heat. Reduce the heat to medium low and simmer until the sauce is slightly reduced and full-flavored, about 5 minutes. Add the vinegar and whole rosemary leaves. Season to taste with salt and pepper. Pour the sauce over the chicken and serve.
Look for a fruity young red with vibrant acidity such as the Michele Chiarlo Barbera d’Asti.