1. Rinse chicken and pat dry; trim and discard pockets of fat. In a bowl, mix vinegar, oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Add thighs; turn to coat. Cover and chill 1 hour.
2. Set a 5- to 6-quart ovenproof pan with lid over medium-high heat. Lift chicken thighs from marinade (reserve marinade) and arrange in a single layer in pan. Turn as necessary to brown on both sides, 4 to 6 minutes total. Transfer chicken to a rimmed plate and lower heat under pan. Add shallots and garlic to pan and stir frequently until shallots are limp, about 5 minutes. Return chicken to pan and add marinade, lemons, vermouth, and herbes de Provence.
3. Cover pan. Transfer to a 350° regular or convection oven and bake until chicken is very tender when pierced, 30 to 45 minutes. Add salt and pepper to taste. Spoon into bowls to serve.
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