Heat oil and 2 tablespoons of broth in wok over medium high heat. Stir in garlic and scallions and stir fry for 30 seconds. Add chicken and sauté for 5 to 8 minutes, until chicken is not longer pink on inside.
Push chicken up edges of wok and pour small amount of broth in the middle.
Add carrots and cook 2 more minutes.
Add asparagus and cook for 3 minutes.
Add water chestnuts and cook 2 minutes.
Mix chicken with vegetables, stirring for 1 minute.
In small bowl, whisk soy sauce, vinegar, oil, broth, and cornstarch. Pour over chicken and mix well.
Place lid over wok and simmer for 2 minutes. Serve