Heat olive oil in a large, heavy cast-iron skillet or Dutch oven over medium-high heat. Season chicken thighs with salt and black pepper. Brown chicken in the hot oil, about 5 minutes per side. Meat will still be pink inside.
Transfer chicken into a bowl, leaving drippings in skillet.
Turn heat down to medium; cook fennel, onion, and fennel seeds in the hot oil, stirring occasionally, until onion and fennel begin to caramelize, about 10 minutes. Stir garlic, thyme, and chile de arbol pepper into fennel mixture. Cook until garlic is fragrant, about 1 more minute. Stir white wine into fennel mixture, scraping up and dissolving any browned bits of food on the bottom of the skillet.
Pour tomatoes with puree into skillet and bring to a boil. Break tomatoes into large chunks with a wooden spoon; adjust salt and pepper.
Add chicken thighs, any accumulated drippings from chicken, and olives to the skillet and stir to combine.
Bake uncovered in the preheated oven until the chicken thighs are no longer pink inside, about 45 minutes.
Let cool 5 to 10 minutes before serving.
Sprinkle with fennel greens, flat-leaf parsley, and lemon zest.
