In a medium saucepan combine rice, 2 cups water, and salt. Bring to a boil over high heat, cover, and reduce the heat to medium-low to cook until rice is tender, about 15 minutes. Turn off the heat and let stand for 5 minutes.
While the rice cooks, in a small bowl whisk together soy sauce, sugar, sesame oil, and cornstarch. Set aside.
Heat 1 tablespoon oil in a large skillet (preferably nonstick) over medium-high heat. Add broccoli and cook until bright green and no longer frozen, about 5 minutes. Add bell pepper and cook until tender, about 1 minute more. Transfer to a bowl and return skillet to the heat. Add 1 tablespoon oil to the skillet, then chicken and cook, stirring frequently, until chicken is no longer pink, about 5 minutes.
Return vegetables to the skillet. Stir the soy sauce mixture to disperse the cornstarch and add it to the pan, stirring to coat the meat and vegetables. Remove from the heat as soon as the sauce thickens and serve over rice. Sprinkle with sesame seeds.