Avoid overcooking this curry—you want the green beans and zucchini to stay bright and beautiful. That said, any leftovers are delicious reheated the next day. Slideshow: More Curry Recipes
Heat the oil in a large skillet over moderately high heat. Add the onion and cook, stirring occasionally, until it begins to soften, about 3 minutes. Add the chile and cook for 1 minute. Add the curry paste and 1/2 cup of the coconut milk and bring to a simmer, stirring until the curry paste has completely dissolved.
Add the rest of the coconut milk and bring to a simmer. Add the green beans and simmer, stirring occasionally, until they are bright green, 3 to 4 minutes.
Add the zucchini and chicken and simmer until the chicken is cooked through and the zucchini is crisp-tender, 5 to 8 minutes. Stir in the fish sauce and lime juice, then serve the chicken garnished with basil leaves, with rice and lime wedges on the side.