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1
Adjust oven rack to lower-middle position; heat oven to 300 degrees.
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2
Sprinkle both sides of chicken with salt.
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3
Heat 1 teaspoon oil in Dutch oven over medium-high heat until shimmering but not smoking.
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4
Add 4 chicken thighs, skin-side down, and cook without moving them until skin is crisp and well browned, about 5 minutes.
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5
Using tongs, turn chicken pieces and brown on second side, about 5 minutes longer; transfer to large plate.
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6
Add remaining 4 chicken thighs to pot and repeat, then transfer to plate and set aside.
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7
Discard all but 1 tablespoon fat from pot.
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8
Add onion to fat in Dutch oven and cook, stirring occasionally, over medium heat until browned, about 4 minutes.
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9
Add garlic, anchovy, and cayenne; cook, stirring constantly, until fragrant, about 1 minute.
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10
Add wine and scrape up browned bits from pan bottom with wooden spoon.
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11
Stir in chicken broth, tomatoes, tomato paste, thyme, oregano, bay, and herbes de Provence (if using).
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12
Remove and discard skin from chicken thighs, then submerge chicken in liquid and add accumulated chicken juices to pot.
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13
Increase heat to high, bring to simmer, cover, then set pot in oven; cook until chicken offers no resistance when poked with tip of paring knife but still clings to bones, about 1 1/4 hours.
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14
Using slotted spoon, transfer chicken to serving platter and tent with foil. Discard bay leaf.
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15
Set Dutch oven over high heat, stir in 1 teaspoon lemon zest, bring to boil, and cook, stirring occasionally, until slightly thickened and reduced to 2 cups, about 5 minutes.
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16
Stir in olives and cook until heated through, about 1 minute.
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17
Meanwhile, mix remaining 1/2 teaspoon zest with parsley.
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18
Spoon sauce over chicken, drizzle chicken with remaining 2 teaspoons olive oil, sprinkle with parsley mixture, and serve.
