Heat oil in a large stir fry skillet set to medium heat. Add garlic and cook 30 seconds.
Add vegetables to skillet and cook, covered, 5 minutes. Transfer vegetables to another bowl or plate and set aside.
Mix together chicken broth, brown sugar, and Worcestershire sauce using the pan in which you cooked the vegetables. Allow to cook 30-60 seconds or until the brown sugar is melted, mixing as it cooks.
Add chicken to the sauce in the pan. Cook chicken covered, about 8-10 minutes or until the chicken is thoroughly cooked, flipping chicken half-way through. (Cooking time will vary based on the thickness of the pieces of chicken.) Remove chicken from the pan.
Mix cornstarch and water together and add to the broth mixture. Bring to a boil and cook 1 minute or until thickened.
To serve, divide the vegetables evenly between 4 plates (about 1/3 to 1/2 cup on each plate). Add one chicken breast to each plate. Pour sauce over the chicken and vegetables (about 1 to 1-1/2 tablespoons per each serving).