Into a large, deep skillet or paella pan over medium-high heat, add 2 tablespoons of olive oil. When the oil is hot, add the chicken. Season with paprika, salt, and pepper. Cook for 5 minutes, turning to brown on both sides. Transfer the chicken to a cutting board and cut into 1-inch pieces. Do not wipe out the pan.
Add the chorizo to the pan and cook for 5 minutes, turning on both sides. Transfer the cooked chorizo slices to the cutting board with the chicken.
Using the same pan, add the remaining 1 tablespoon of olive oil. When the oil is hot, add the onion and peppers. Cook for 2 minutes, until softened. Add the garlic and continue cooking for an additional 1 minute.
Add the chicken-style broth, saffron threads, and rice. Give the rice 1 good stir around the pan, just enough to cover completely with the liquid. Bring to a low boil then reduce the heat to low. Cover and simmer for 15 minutes, until the rice is cooked.
Gently stir in the chicken, chorizo, and peas. Continue cooking, undisturbed, for 5 more minutes to get a light crust on the bottom of the rice then serve.