Preheat oven to 425°F. In a small saucepan, bring chicken broth to a boil over high heat. Add saffron, reduce heat, cover and keep barely at a simmer while you proceed.
In a deep, 12-inch ovenproof skillet, heat oil over medium heat. Add chorizo and cook, stirring, for 1 minute. Transfer chorizo to a bowl and set aside. Increase heat to medium-high, add chicken, in batches if necessary, and cook, turning, until golden brown but not thoroughly cooked, about 7 minutes. Add chicken to chorizo.
Put yellow peppers, onion, garlic, salt and pepper in skillet and cook over medium heat, stirring, until peppers are softened, about 3 minutes. Stir in paprika. Add half of tomatoes and half of parsley and cook, stirring, for 1 minute.
Add rice and stir to coat well. Pour in warm broth and bring to a boil. Boil for 3 minutes, stirring occasionally, until rice is no longer soupy but there is enough liquid to continue to cook rice. Return chicken and chorizo to skillet. Add remaining tomatoes and top with mussels.
Transfer skillet to oven and cook until rice is almost al dente, about 10 minutes. Stir or tuck in shrimps, and cook for 5 minutes longer. Remove skillet from oven, cover tightly with foil, and let stand for 15 minutes or until rice is fully cooked. Sprinkle remaining parsley on top, and serve dish hot.