Heat olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper. Cook and stir chicken in hot oil until cooked through and juices run clear, 5 to 7 minutes. Add the broth and salsa and bring to a boil; turn off the heat and stir in the instant rice. Sprinkle Cheddar cheese over the mixture. Cover the skillet and let sit until the rice is tender, about 5 minutes.
