Season chicken thighs generously with salt and pepper on both sides. Let rest at room temperature for 10 minutes.
Heat olive oil in large skillet over medium-high heat. Place chicken skin-side down and sear undisturbed for 6 to 7 minutes until golden. Flip and cook 5 more minutes. Remove to plate.
Add sliced sausage to same skillet. Cook 4 to 5 minutes until browned. Drain excess grease, leaving 2 tablespoons.
Add minced garlic and sauté for 30 seconds until fragrant.
Stir in bell peppers and cherry peppers. Cook 3 to 4 minutes until peppers begin to soften.
Pour in white wine and scrape up browned bits. Simmer 2 to 3 minutes until reduced by half.
Add chicken broth, cherry pepper vinegar, lemon juice, and oregano. Stir and bring to simmer.
Return chicken to skillet skin-side up. Spoon sauce over top. Cover partially and simmer 20 to 25 minutes until chicken reaches 165°F internal temperature.
Taste and adjust seasoning. Serve hot with sauce and peppers spooned over chicken.
Notes
Bone-in chicken thighs stay juicier and add richer flavor. Boneless works but reduce cooking time to 15 to 18 minutes.
Cherry pepper vinegar from the jar is essential for authentic tangy flavor.
Dish tastes even better the next day after flavors meld together.
Freezes well for up to 2 months in airtight containers.