Heat olive oil in a large high-sided skillet over medium-high heat. Pat chicken dry and season on both sides with salt and pepper. Once oil is hot, brown the chicken for 4 minutes on each side. Remove the chicken from the pan to a plate.
Add onion and garlic to the pan and sauté until tender, about 3 to 4 minutes. Season with salt and pepper. Sprinkle in smoked paprika and stir to toast. Add rice and sauté for 1 minute, then stir in the wine and scrape up any browned bits on the bottom of the pan. Add tomatoes and chicken stock and bring to a simmer.
Nestle chicken into the rice and pour in any drippings left over on the plate. Cover with lid and place in the oven for 40 minutes. Remove lid, sprinkle in peas, and continue baking for 5 more minutes, until all the liquid is absorbed.