Rinse the jasmine rice under cold water in a fine-mesh sieve until the water runs clear to remove excess starch.
In a small saucepan, combine the rinsed rice with 1.5 tablespoons of the coconut milk and 0.5 cup of water.
Bring the rice to a boil, then reduce the heat to low, cover with a tight-fitting lid, and simmer for 15 minutes.
While the rice cooks, dice the chicken breast into bite-sized pieces and season them with the sea salt and black pepper.
Heat the coconut oil in a large skillet or wok over medium-high heat and sear the chicken until golden and cooked through.
Remove the cooked chicken from the skillet and set aside; add the green curry paste to the same skillet and sauté for 1 minute until fragrant.
Whisk in the remaining 1.5 tablespoons of coconut milk and 2 tablespoons of water to create a smooth curry sauce base.
Add the snap peas and sliced red bell pepper to the skillet, simmering for 3 minutes until the vegetables are tender-crisp.
Return the chicken to the skillet, stirring in the fish sauce and lime juice to balance the flavors.
Fluff the coconut rice with a fork and serve the green curry chicken over the top, garnished with fresh cilantro.