Dry chicken and season with salt and pepper. Put the oil in a large, heavy-bottomed skillet over medium-high heat. When it’s hot, add the chicken, skin side down. Cook, undisturbed until the chicken is golden brown and releases easily from the pan, 7 to 10 minutes. Then turn and brown the other side, 5 minutes more. Remove from the pan and set aside.
Reduce the heat under the skillet to medium and pour or spoon off most of the oil so that only 2 tablespoons remain. Add the onions to the pan and cook, stirring frequently, until soft and golden, 3 to 5 minutes. Add the garlic and smoked paprika and cook for another minute. Pour the rice into the pan and stir until coated with oil and slightly toasted. Add wine and stir until it’s mostly absorbed, 3 minutes. Add chicken stock and the Peri-Peri sauce and stir everything together.
Bring the mixture to a boil, then return the chicken to the pan, skin-side up, reduce the heat so it bubbles gently but steadily. Cover the skillet and cook, undisturbed, for 20 minutes, then check the rice and chicken. You want to have the liquid absorbed, the rice tender, and the chicken just cooked through. (If all the liquid is absorbed before the chicken is ready, add another 1/4 cup water or stock and cook for another 5 to 10 minutes). The meat is done when a quick-read thermometer inserted into the thickest part of the thigh reads 155–165°F.
Remove the skillet from the heat. Taste the rice and adjust the seasoning. Add the peas, then cover the pan again and let it sit for 5 to 15 minutes. Remove the chicken and transfer it to a serving platter. Fluff the rice with a fork, spoon it around the chicken, sprinkle over the cilantro, add the lime wedges, and serve with extra Peri Peri sauce on the side.