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1
Preheat oven to 425u00b0F. Very thinly slice half of lemon; discard any seeds. Cut remaining lemon half into 2 wedges. Season chicken thighs with salt and pepper.
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2
Coat a large room-temperature skillet with 1 teaspoon oil. Add chicken, skin side down. Place skillet over medium heat and cook, letting skin render and brown, and pouring off excess fat to maintain a thin coating in pan, until chicken is cooked halfway through, about 10 minutes.
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3
Scatter half of lemon slices over chicken and half on bottom of skillet (the slices on top of the chicken will soften; those in the skillet will caramelize). Transfer skillet to oven, leaving chicken skin side down. Roast until chicken is cooked through, skin is crisp, and lemon slices on bottom of skillet are caramelized, 6-8 minutes.
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4
Transfer chicken pieces, skin side up, and caramelized lemon slices from bottom of skillet to a warm platter. (Leave softened lemon slices in the skillet.) Return skillet to medium heat. Add oregano sprigs, shallot, garlic, and red pepper flakes; cook, stirring frequently, until fragrant, about 1 minute.
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5
Remove skillet from heat. Add wine; cook over medium heat until reduced by half, 1-2 minutes. Add broth; cook until thickened, about 3 minutes. Squeeze 1 lemon wedge over and season sauce with salt, pepper, and juice from remaining lemon wedge, if desired. Drizzle with 2 teaspoons oil. Return chicken to skillet, skin side up, to rewarm. Serve topped with caramelized lemon slices.
