Rinse jasmine rice until water runs clear.
In a small pot, combine rice, 0.5 cup water, 1 tbsp coconut milk, and a pinch of sea salt; bring to a boil, then simmer covered for 15 minutes.
Heat coconut oil in a large skillet over medium-high heat.
Add sliced chicken breast and sauté until golden brown and cooked through.
Stir in green curry paste and cook for 1 minute until aromatic.
Pour in the remaining 1 tbsp coconut milk and 0.25 cup water, stirring to combine.
Add sliced bell peppers and snap peas, simmering for 3-4 minutes until the vegetables are tender-crisp.
Stir in fish sauce, lime juice, and coconut sugar to balance the flavors.
Serve the curry over the fluffy coconut rice.