Pat the chicken thighs dry with paper towels. This helps achieve a crisp, golden-brown sear. Season both sides generously with salt and a light dusting of dried oregano.
In a large skillet, heat olive oil over medium-high heat. When hot, place the chicken thighs skin-side down and cook until the skin is deeply golden and crisp, about 6–8 minutes. Flip and sear the other side for 4–5 minutes, then transfer to a plate.
Reduce the heat to medium. Add the butter to the same skillet. Once melted, add minced garlic and red pepper flakes. Sauté for about 30-45 seconds until fragrant, being careful not to burn the garlic.
Zest half of the lemon over the pan, then squeeze in the juice (remove seeds). Deglaze the pan with the chicken broth, scraping up any browned bits for maximum flavor.
Return the chicken thighs to the skillet. Scatter capers and olives around them. Spoon some of the sauce over the chicken to coat. Simmer for 6–8 minutes until the chicken reaches an internal temperature of 165°F (74°C) and the flavors meld.
Stir in chopped parsley and a final squeeze of lemon juice to brighten the sauce. Taste and adjust salt if needed. If you’d like a thicker sauce, simmer for an extra minute or two until it coats the back of a spoon.
Serve the chicken with a generous spoonful of the lemon-garlic butter pan sauce, alongside a simple side like roasted vegetables, couscous, or a light greens salad.