In a small saucepan, combine the jasmine rice, 1 tablespoon of coconut milk, and 0.5 cup water; bring to a boil, then reduce heat and simmer covered for 15 minutes.
While rice cooks, heat the coconut oil in a large skillet over medium-high heat.
Add the sliced chicken breast to the skillet and sear until golden brown, approximately 3-4 minutes per side.
Stir in the green curry paste and cook for 1 minute until the aromatic oils are released and fragrant.
Pour in the remaining 2 tablespoons of coconut milk, fish sauce, and coconut sugar, stirring to create a smooth sauce.
Add the sliced bell peppers and snap peas to the skillet, simmering for 5 minutes until the vegetables are tender-crisp and the chicken is fully cooked.
Remove the skillet from heat and stir in the fresh lime juice and Thai basil leaves.
Fluff the coconut rice with a fork and serve the green curry over the rice, finishing with a pinch of sea salt.