Stir water into cornstarch in small cup. Set aside.
Heat large frying pan or wok on medium high until very hot. Add cooking oil. Add chicken. Stir fry for about 5 minutes until browned. Add carrots and cook until tender. Add red peppers if you desire.onions or broccoli.
Combine remaining 6 ingredients in small bowl .Add to chicken mixture. Stir and bring to a boil. Reduce heat to med-low. Simmer, covered, for about 6 minutes until chicken is no longer pink inside and carrot is tender crisp. Stir in cornstarch mixture. Heat and stir for about 1 minute until boiling and thickened.