Rinse the jasmine rice under cold water and place in a small saucepan with 0.4 cups of the water, 1 tablespoon of the coconut milk, and a pinch of salt.
Bring the rice to a boil, then reduce heat to low, cover, and simmer for 15 minutes until fluffy and tender.
Slice the chicken breast into thin bite-sized strips and thinly slice the red bell pepper.
Heat coconut oil in a large skillet over medium-high heat and sauté the chicken until golden and cooked through, then remove from the pan and set aside.
In the same skillet, add the green curry paste and stir for 1 minute until the aroma is released and the paste is slightly darkened.
Whisk in the remaining 1 tablespoon of coconut milk, 0.5 cups of water, fish sauce, and coconut sugar, bringing the mixture to a gentle simmer.
Add the red bell pepper and sugar snap peas to the sauce, cooking for 3 minutes until the vegetables are tender yet crisp.
Return the cooked chicken to the skillet, stir in the lime juice and fresh basil, and serve immediately over the prepared coconut rice.