Rinse the jasmine rice under cold water until the water runs clear.
In a small saucepan, combine the rice, water, and one tablespoon of the coconut milk; bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes.
While the rice cooks, slice the chicken breast into thin strips and season with sea salt and black pepper.
Heat the coconut oil in a large skillet over medium-high heat.
Add the chicken to the skillet and sauté until browned and cooked through, about 5 minutes, then remove the chicken and set aside.
In the same skillet, add the green curry paste and stir for 1 minute until highly fragrant.
Whisk in the remaining coconut milk, fish sauce, and coconut sugar until the sauce is smooth.
Add the green beans and sliced red bell pepper to the sauce and simmer for 4 minutes until the vegetables are tender-crisp.
Return the cooked chicken to the skillet and toss to coat thoroughly in the green curry sauce.
Fluff the coconut rice with a fork and serve the chicken and vegetables over the rice, garnished with fresh cilantro.