Add 2 tablespoons of the oil and heat for 30 seconds. Add the chicken and stir-fry until cooked through, 3 to 4 minutes. Transfer to a plate. Wipe out the pan.
Reduce heat to medium-high, add the remaining oil, and heat for 30 seconds.
Add the carrots and water. Cover partially and cook, stirring occasionally, until almost tender, about 2 minutes. Add the bok choy stems, cover, and cook for 2 minutes. Add the bok choy leaves and peas and toss gently. Add the Cantonese Light Sauce and increase heat to high.
When it starts to bubble, add the chicken. Stir-fry until warmed through, about 1 minute.