Pulse the onions and parsley in a food processor until finely chopped. In a large, heavy saucepan, heat 2 tablespoons olive oil over medium heat, add the onion mixture and cook for 3 minutes. Stir in the rice and broth and bring to a boil. Lower the heat, cover and simmer for 15 minutes.
Meanwhile, add the remaining 2 tablespoons olive oil to the skillet. Season the chicken with salt and pepper and add to the skillet. Cook the chicken for about 3 minutes on each side. Add to the rice along with the peas and half of the almonds. Cover the rice and cook until heated through, about 5 minutes. Stir in the lime juice; season with salt and pepper to taste. Spoon into bowls and top with the remaining almonds.