Heat 1 tablespoon oil in a 10-inch skillet over medium-high heat.
Add the chicken and cook for 10 minutes or until well browned on both sides.
Remove the chicken from the skillet.
Heat the remaining oil in the skillet over medium heat.
Add the eggplant and zucchini and cook for 2 minutes, stirring occasionally. Stir in the water and sauce and cook for 2 minutes, stirring occasionally.
Stir in the oregano. Return the chicken to the skillet. Reduce the heat to low. Cover and cook for 5 minutes or until the chicken is cooked through.
Place the rice onto a serving platter. Slice the chicken and place it on the rice. Spoon the sauce mixture over the chicken and sprinkle with the cheese and parsley.