Heat the oil in a large skillet over medium-high heat. Add the chicken pieces; cook and stir for about 3 minutes. Mix in the curry paste, zucchini, bell pepper, carrot and onion. Cook and stir for a few minutes.
Dissolve the cornstarch in the coconut milk, then pour into the skillet. Bring to a boil, then simmer over medium heat for 1 minutes. Right before serving, stir in the cilantro.
