Rinse the jasmine rice under cold water until clear, then combine in a small saucepan with 0.125 cup of the coconut milk and 0.25 cup water.
Bring the rice to a boil, then reduce heat to low, cover, and simmer for 15 minutes until the liquid is absorbed and rice is fluffy.
While the rice cooks, heat the coconut oil in a large skillet or wok over medium heat and sauté the green curry paste for 1 minute until highly aromatic.
Whisk in the remaining 0.125 cup of coconut milk and bring the mixture to a gentle simmer.
Add the thinly sliced chicken breast, sliced red bell peppers, and sugar snap peas to the curry sauce.
Stir in the fish sauce, coconut sugar, and kaffir lime leaves, then continue to simmer for 5-7 minutes until the chicken is cooked through and vegetables are tender-crisp.
Remove the skillet from the heat and stir in the fresh Thai basil leaves.
Serve the green curry chicken immediately over the warm coconut rice.