In a re-sealable plastic bag, combine the garlic, mustard, vinegar, oil, salt and chicken. Press out the air and seal tightly. Swish the chicken around until it’s fully coated in the marinade. Refrigerate for at least 2 hours or overnight.
Preheat the oven to 375 degrees F.
Arrange the tomatoes, shallots, olives, capers, and dates in a large casserole or baking dish (9 x 13 or comparable). Nestle the chicken in the vegetables, scraping as much of the marinade as possible into the baking dish. Tuck the oregano sprigs, if using, between the chicken thighs. Pour the wine over the vegetables and chicken.
Bake in the oven for 1 hour, or until the chicken is tender, browned on top, and the vegetables are caramelized.