Combine teriyaki sauce and sugar in measuring cup, stirring until sugar dissolves.
Remove 3 tablespoons of mixture and set aside.
Pour rest of marinade over chicken in large plastic food storage bag. Press air out of bag; close top securely. Turn bag over several times to coat pieces well. Marinate 15 minutes.
Add enough water to remaining 3 tablespoons teriyaki sauce mixture to measure 2/3 cup; blend in cornstarch.
Heat oil in large skillet over medium-high heat; add chicken and saute 5 minutes or until chicken is thoroughly cooked through. Add teriyaki sauce mixture; cook, stirring, about 1 minute, or until sauce boils and thickens slightly.
Spoon chicken and sauce over rice in large individual serving bowls. Serve vegetables on top of rice or on the side, as desired.