In a large skillet, heat 2 tablespoons of the oil. Add the chicken, season with salt and pepper and cook over high heat until just white throughout, 2 minutes. Transfer the chicken to a plate.
Add the remaining oil to the skillet. Add the onion and stir-fry over moderately high heat for 2 minutes. Add the zucchini and cherry tomatoes and stir-fry for 2 minutes. Stir in the curry paste, coconut milk, water, lime zest and lime juice and bring to a simmer. Add the chicken and stir for 20 seconds. Stir in the cilantro. Transfer to bowls and serve with rice.