Heat 1 tablespoon of vegetable oil in a large pan over medium-high heat. Add the chicken breast slices and cook until golden brown and cooked through, about 5-6 minutes. Remove from the pan and set aside.

In the same pan, add the remaining tablespoon of oil. Add the garlic and ginger, sautéing until fragrant, about 1 minute.

Add the carrots and cabbage to the pan and stir-fry for 3-4 minutes, or until the vegetables are tender-crisp.

Meanwhile, cook the chow mein noodles according to the package instructions. Drain and add them to the pan with the vegetables.

In a small bowl, combine soy sauce, oyster sauce, and sugar. Pour the sauce over the noodles and vegetables, tossing to coat evenly.

Return the cooked chicken to the pan, and stir everything together until heated through and well combined. Serve hot.