In a four quart saucepan, bring the chicken stock to a simmer.
In a Dutch oven, heat the oil on medium heat and cook the smoked paprika and tomato paste for a minute. Then add the rice and stir it until it is well coated with the oil and spices. Add a quarter cup of the stock, stirring the rice with a wooden spoon.
When the rice begins to stick to the bottom of the pot, and another quarter cup of stock. Keep adding the stock in quarter cup increments until the rice is almost tender. You may not need all of the stock. Add the shrimp, chorizo, and peas and cook until the shrimp is fully cooked, about five minutes.