In a medium-sized skillet over medium heat, melt the butter.
Add the zucchini, onion, carrots, and peas and cook until slightly browned and tender, about 7 minutes. Remove the vegetables to a plate and set aside.
To make the sauce, stir together the soy sauce, water, garlic, brown sugar, and cornstarch.
Pour 4 tbsp of the sauce over the cubed chicken in a bowl, stir, and add evenly to the hot pan. Cook until the chicken is browned and cooked through, about 8-10 minutes.
Add the rest of the sauce and the vegetables back to the pan. Cook until thickened and reduced, about 5 minutes.
Serve hot over rice.