Heat oven to 400° F.
Pat the chicken dry with a paper towel and season with 1 teaspoon salt and 1/2 teaspoon pepper. Heat the oil in a large ovenproof saucepan over medium-high heat. Add the chicken, skin-side down, and cook until the skin is crisp, about 5 minutes. Turn the chicken and add the broth, paprika, and onions. Transfer to oven and cook, uncovered, for 30 minutes.
Add the gnocchi and continue cooking until the gnocchi are cooked through, about 15 minutes. Divide among individual plates.