In a large saucepan, heat the olive oil. Add the onion and cook over moderate heat, stirring occasionally until tender, about 6 minutes. Add the smoked paprika, oregano and cumin and cook for 1 minute, until fragrant. Add the chicken broth, rice and chicken meat, bring to a boil, cover and simmer over low heat for 18 minutes. Remove from the heat, add the peas, cover and let stand 5 minutes. Using a fork, fluff the rice and season with salt and pepper. Spoon the rice into bowls, sprinkle with cilantro and serve with lime wedges.