Combine jasmine rice, 1 tablespoon of coconut milk, a pinch of sea salt, and 0.5 cup of water in a small pot; bring to a boil, then cover and simmer on low for 15 minutes.
While the rice cooks, slice the chicken breast into thin, bite-sized strips and thinly slice the red bell pepper.
Heat avocado oil in a large skillet over medium-high heat and sear the chicken strips until golden and cooked through, about 5 minutes.
Stir the green curry paste into the skillet and cook for 1 minute until the aroma is released.
Pour in the remaining 1.5 tablespoons of coconut milk along with the red bell pepper and sugar snap peas.
Simmer the curry for 5 minutes until the vegetables are tender-crisp and the sauce has slightly thickened.
Stir in the fish sauce and coconut sugar to balance the flavors, then remove from heat.
Fluff the coconut rice with a fork and portion it into a bowl.
Spoon the chicken and green curry over the rice and garnish with fresh cilantro and a squeeze of lime.