Place all green curry paste ingredients in a food processor plus 3 tablespoons of the coconut milk (leave the rest in the can, you'll use it in a moment)
Process until fragrant and smooth. Set aside.
Warm a wok or large frying pan over medium-high heat and add the oil. Swirl the heated oil around.
Add all of the green curry paste and stir-fry briefly to release the fragrance, about 1 minute.
Add about ¾ of the remaining coconut milk, leaving the rest for later.
Stir-fry together with the paste, blending the two.
Add the chicken, stirring to incorporate. When the curry sauce begins to boil, reduce the heat to a simmer.
Let simmer for about 8 minutes, until chicken is cooked through, stirring occasionally.
Add the zucchini and the strips of lime leaves, stirring well to incorporate.
Simmer for another 3 minutes.
Remove from heat and taste test...you want a nice balance of salty, spicy, sweet and sour. Adjust flavors with fish sauce, or sugar...if too sweet, add a tablespoon of lime juice.
Portion out into individual serving bowls, topping each one with a generous sprinkling of the basil.
Finally, drizzle over 2-3 tablespoons (per bowl) of the reserved coconut milk.
Serve with jasmine rice