Rinse the jasmine rice under cold water until the water runs clear to remove excess starch.
In a small saucepan, combine the jasmine rice, water, sea salt, and 2 tablespoons of the coconut milk; bring to a boil, then cover and simmer on low for 15 minutes.
While the rice cooks, slice the chicken breast into thin, bite-sized strips.
Heat the coconut oil in a large skillet or wok over medium heat and sauté the green curry paste for 1 minute until fragrant.
Whisk in the remaining coconut milk, fish sauce, and coconut sugar, bringing the liquid to a gentle simmer.
Add the chicken strips to the skillet and cook for 5-6 minutes until the chicken is nearly cooked through.
Toss in the sliced red bell pepper and sugar snap peas, simmering for another 3 minutes until the vegetables are tender-crisp.
Stir in the lime juice and fresh basil leaves just before removing the skillet from the heat.
Fluff the coconut rice with a fork and serve the green curry chicken over the top.