Boil chow mein noodles according to package instructions, drain, and set aside.
Slice chicken breast into thin strips and season lightly with salt and pepper.
Heat oil in a wok or skillet over medium-high heat; stir-fry chicken until cooked through. Remove and set aside.
In the same pan, add garlic, cabbage, carrot, and green onions; stir-fry until crisp-tender.
Mix oyster sauce, soy sauce, sesame oil, chicken broth, cornstarch, and sugar to make the sauce.
Return chicken to the pan, add cooked noodles and sauce; toss everything together and cook until sauce thickens and coats the noodles evenly.
Serve hot, optionally with a fresh Cucumber Salad or a refreshing Disaronno Drink.