Place olive oil in a paella pan or 16-inch skillet over medium-high heat. Season both sides of the chicken with salt and pepper. Sauté chicken pieces until golden, 4 minutes on the first side, 2 minutes on the second. Remove chicken from pan and set aside.
Add onion to the pan and sauté until translucent. Add tomatoes, crushing them with the back of a spoon, then add peppers, olives, capers, bay leaves, saffron, and sauté for 5 minutes.
Add rice and stir to distribute, then add stock and stir. Return chicken pieces to the pan, skinned side up, pushing them into the rice. Bring to a boil, then reduce heat and simmer for 30 minutes. Sprinkle with parsley. Serve in the pan at the table.
Notes
Traditionally, arroz con pollo is made with Bomba rice, even more elusive than the alcapparado. You can use Arborio rice.It would most likely have also had some pimentón (Spanish smoked paprika), but it wasn't widely available in the day, and I like sticking to Jacques's recipe.