1. Heat 1 tablespoon of the olive oil in a large nonstick skillet until shimmering. Season the chicken thighs with salt and pepper and cook over moderately high heat until browned on both sides, about 12 minutes. Transfer to a plate.
2. Heat the remaining 3 tablespoons of olive oil in an enameled cast-iron casserole until shimmering. Add the potatoes and cook over moderately high heat until golden, about 10 minutes. Stir in the fennel pollen and cook until fragrant, about 30 seconds. Add the tomatoes and water, season with salt and pepper and bring to a boil. Return the chicken to the casserole, cover partially and cook over moderately low heat until the chicken is cooked through, about 20 minutes. Serve hot.
Make Ahead: The chicken stew can be refrigerated overnight.