Rinse the jasmine rice under cold water until the water runs clear to remove excess starch.
In a small saucepan, combine the rice, 2 tablespoons of the coconut milk, water, and sea salt; bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes.
While the rice is cooking, heat the coconut oil in a large skillet or wok over medium-high heat.
Add the sliced chicken breast to the skillet and sear until golden brown on the outside, about 3-4 minutes.
Stir in the green curry paste and cook for 1 minute until the aromatics are released and fragrant.
Pour in the remaining coconut milk and add the green beans and sliced red bell peppers to the skillet.
Lower the heat and simmer for 5-7 minutes until the chicken is cooked through and the vegetables are tender-crisp.
Stir in the fish sauce and lime juice to balance the flavors of the curry.
Remove the rice from heat and fluff with a fork to incorporate the coconut cream.
Serve the green curry chicken over a bed of coconut rice and garnish with fresh cilantro.