Heat the oil in a Dutch oven or large saucepan over medium-high heat. Season the chicken with ½ teaspoon salt and ¼ teaspoon black pepper. In 2 batches, brown the chicken, 5 to 7 minutes per side; transfer to a plate.
Add the onion and bell pepper to the drippings in the Dutch oven and cook, stirring often, until beginning to soften, 3 to 5 minutes. Add the rice, broth, thyme, and chicken. Bring to a boil, reduce heat, and simmer, covered, until the chicken is cooked through, the rice is tender, and most of the liquid is absorbed, 20 to 25 minutes.
Remove the Dutch oven from heat. Transfer the chicken to a plate. Fold the peas and olives into the rice and let sit, covered, for 5 minutes. Serve with the chicken.