Pour the vinegar into a blender jar, followed by the salt, turmeric, onion, garlic and chiles. Purée, scraping the inside of the jar as needed, to make a smooth, yellow-hued light purple marinade.
Place the chicken in a baking dish and spoon the marinade over it, turning the chicken pieces to coat them thoroughly. Refrigerate, covered, for at least 30 minutes or up to 2 hours, to allow the flavors to penetrate the meat. (Because vinegar is so acidic, you do not want to marinate the chicken for any longer because it might break down the meat's texture, rendering it unappetizing.)
Heat the oil in a large skillet over medium-high heat. Add the chicken, including the marinade, meat side down, in a single layer. Cook, allowing the meat to sear after some of the nose-tingling marinade boils off, until browned, 5 to 7 minutes. Turn the chicken over and brown on the other side, about 5 minutes.
Pour in the coconut milk and lift the chicken pieces slightly to allow it to coat the bottom of the skillet and to loosen the browned bits, deglazing the skillet.
Add the diced tomatoes, with their juice, stirring to incorporate them into the curry. Once it comes to a boil, reduce the heat to medium-low, cover and simmer, turning the chicken pieces occasionally and basting them every 3 to 4 minutes, until the meat in the thickest parts is no longer pink inside and the juices run clear, 20 to 25 minutes. Transfer the chicken to a serving platter.