Special equipment: a 5 1/2-quart Dutch oven
Preheat a large Dutch oven over medium-high heat. Add the oil and let it get nice and hot. Add the chorizo; cook until it renders out some fat and crisps around the edges, about 3 minutes. Using a slotted spoon, remove the chorizo to a paper-towel-lined plate. Set aside.
Add the chicken to the pot, sprinkle with a small pinch of salt and pepper, and saute until the chicken develops color all around, 4 to 6 minutes. Remove to a plate and set aside.
Reduce the heat to medium and add the onions, peppers and garlic. Cook until the veggies soften a bit and develop some color around the edges, 5 to 7 minutes. Add the rice and paprika and cook, stirring, until toasted a bit, 1 to 2 minutes.
Add the stock and tomatoes and the cooked chorizo and chicken; bring to a boil. Allow the rice to absorb the liquid for 5 minutes--the rice should peak through liquid--then stir and turn the heat down to medium-low. Cover and cook for about 25 minutes or so, until the rice is fully cooked. Adjust the seasoning to taste.
Add the peas, olives and some chopped parsley. Fluff everything together with a fork. Scatter some more parsley over the top and enjoy!