Season the chicken with 1/2 teaspoon of salt and the paprika.
Heat the oil in a large, deep skillet or sauté pan with a lid over medium-high heat. Add the chicken in a single layer and brown for 3–4 minutes, turning once. It does not need to cook through. Transfer to a plate.
Lower the heat to medium. Add the onion and pepper and cook for 4 minutes, then the zucchini and garlic for 2 minutes more.
Stir in the rice to coat it with oil, then add the broth, tomatoes, remaining salt and the chicken with its juices. Bring to a boil.
Cover, reduce the heat to low and simmer for 18 minutes without lifting the lid.
Scatter the peas over the top, cover again, remove from the heat and let stand for 10 minutes. Fluff with a fork, check that the chicken is cooked through (165°F / 74°C), and serve with lemon and parsley.