Warm a wok or large frying pan over medium-high heat. Add oil and swirl around, then add the green curry paste.
Stir-fry briefly to release the fragrance (30 seconds to 1 minute), then add coconut milk.
Add chicken, stirring to incorporate. When the curry sauce comes to a boil, reduce heat to medium or medium low, until you get a nice simmer.
Cover and allow to simmer 3-5 more minutes, or until chicken is cooked through. Stir occasionally.
Add the bell pepper and zucchini, plus the lime zest, stirring well to incorporate. Simmer another 2-3 minutes, or until vegetables are softened but still firm and colorful.
Do a taste test for salt, adding 1-2 T. fish sauce if not salty enough. If you would prefer a sweeter curry add a little brown sugar. If too salty, add a squeeze of lime juice. If too spicy, add more coconut milk.
Serve this curry in bowls over rice. Top each portion with fresh basil.