Heat the olive oil in a large heavy skillet or pot over high heat.
Add the onion and garlic and cook, stirring, until the onion is translucent, about 3 minutes. Season the chicken with 1/4 teaspoon each salt and pepper.
Add to the skillet along with the chorizo; cook, turning occasionally, until the chicken starts to brown, about 3 minutes. Move the chicken and chorizo to one side of the pan and stir in the tomato paste, rice and capers.
Add the broth and bring to a boil. Cook, stirring occasionally, about 8 minutes. Stir in the peas, reduce the heat to medium low, cover and cook until the rice is tender, about 15 minutes.
Let rest, covered, 5 minutes. Fluff the rice with a fork, stirring to combine all the ingredients.