Rinse the jasmine rice under cold water until the water runs clear.
In a small saucepan, combine the rice, water, and a pinch of salt; bring to a boil, then reduce heat to low and simmer covered for 15 minutes.
While the rice cooks, heat the coconut oil in a large skillet over medium-high heat.
Add the chicken breast pieces to the skillet and sauté until lightly browned on all sides.
Stir in the green curry paste and cook for 1 minute until the aromatics are released.
Pour in the coconut milk and fish sauce, stirring to combine the paste into the liquid.
Add the sliced bell peppers and sugar snap peas to the skillet.
Simmer the mixture for 5-7 minutes until the chicken is fully cooked and the vegetables are tender-crisp.
Remove from heat and stir in the fresh lime juice.
Fluff the rice with a fork and serve the green curry over the rice, garnished with fresh cilantro.