Pat the chicken thighs dry with paper towels and season generously with salt and pepper on both sides.
Heat olive oil in your cast-iron skillet over medium-high heat until shimmering and just starting to smoke.
Place the chicken thighs skin-side down and sear, without moving, until golden brown and crispy, about 5-7 minutes.
Flip the chicken and cook for another 5 minutes, then remove from the pan and set aside temporarily.
Add the sliced fennel and minced garlic to the pan. Sauté, stirring frequently, until the fennel is tender and slightly caramelized, about 5 minutes.
Deglaze the pan with white wine or chicken broth, scraping up browned bits from the bottom, and let it simmer for 2 minutes to reduce slightly.
Return the chicken thighs to the skillet, skin-side up if using skin-on, and nestle the artichoke hearts and olives around them.
Cover the skillet and reduce the heat to low. Let everything simmer gently for 20-25 minutes until the chicken is cooked through and tender.
Uncover the skillet and increase heat to medium. Cook for another 3-5 minutes to allow the sauce to thicken slightly and flavors to meld.
Taste and adjust seasoning with salt and pepper as needed. The sauce should be glossy and flavorful, coating the chicken and vegetables evenly.
Serve the chicken thighs hot, spooning the fennel, olives, and artichokes alongside. Enjoy the tender, aromatic bites with crusty bread or a simple salad.