Heat 2 tablespoons of the olive oil in a large skillet over medium-high heat. Add the chicken and saute until cooked through, about 5 minutes. Transfer to a plate.
Add the remaining 2 tablespoons olive oil to the skillet. Add the tomatoes and cook until they start to blister, pop and release their juices, about 3 minutes. Lightly mash them with a wooden spoon or fork. Stir in the artichoke hearts with the marinade, olives and roasted red peppers. Season with salt and pepper and cook until heated through, 2 to 3 minutes. Stir in the parsley and cooked chicken and cook for another minute.
Meanwhile, cook the frozen rice according to the package instructions. Transfer the rice to a serving bowl and top with the chicken mixture.