Wash hands with soap and water for 20 seconds.
Bring rice and water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover and simmer until rice is tender and liquid has been absorbed, 20 to 25 minutes.
Cut chicken breasts into thin strips.
Wash the counter and utensils that touched the raw chicken. Wash hands with soap and water after handling raw chicken.
Meanwhile, combine soy sauce, brown sugar, and cornstarch in a small bowl; stir until smooth. Mix ginger, garlic, and red pepper into sauce. Cover chicken strips with marinade and refrigerate for at least 15 minutes.
Scrub the onion and carrot with a clean vegetable brush under cold running water. Gently rub broccoli and bell pepper under cold running water.
Prepare vegetables as indicated in ingredients.
Heat 1 Tablespoon sesame oil in a large skillet over medium-high heat. Cook and stir onion, carrots, broccoli, bell pepper, and drained water chestnuts until just tender, about 5 minutes. Remove vegetables from skillet and keep warm.
Remove chicken from marinade. Reserve marinade. Heat 1 tablespoon sesame oil in skillet over medium-high heat. Cook and stir chicken until slightly pink on the inside, about 2 minutes per side. Return vegetables and reserved marinade to the skillet. Bring to a boil; cook and stir until chicken is no longer pink in the middle and vegetables are tender, 5-7 minutes. Serve immediately over rice.
Return vegetables and reserved marinade to the skillet. Bring to a boil; cook and stir until chicken is cooked until internal temperature reaches 165°F on a food thermometer and vegetables are tender, 5-7 minutes.
Serve stirfry immediately over rice.