Pat chicken dry. Season with 1 tsp salt, 0.5 tsp pepper, paprika, and oregano.
Heat olive oil in a large deep skillet over medium-high heat.
Brown chicken in two batches until lightly golden, 4–5 minutes per side. Transfer to a plate.
Reduce heat to medium. Sauté onion and carrots in the drippings until softened, about 3 minutes.
Stir in garlic and rice. Toast the rice for 1 minute, stirring often.
Pour in broth and scrape the pan bottom. Return chicken and any juices to the skillet.
Bring to a gentle boil. Cover, lower heat, and simmer until rice is tender, 18–22 minutes.
Stir in peas, butter, and remaining salt and pepper. Cover 2–3 minutes to warm through.
Finish with lemon juice and zest. Fluff the rice and adjust seasoning to taste.
Rest 5 minutes off heat. Sprinkle with parsley and serve hot.