Bring the rice and water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until the rice is tender, and the liquid has been absorbed, 20 to 25 minutes.
Heat the vegetable oil in a large skillet over medium heat. Cook the chicken breasts until no longer pink in the center and the juices run clear, about 25 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Cut the chicken into bite size pieces.
Toss chicken, rice, and lettuce in a large bowl. Serve immediately.
