Place the rice in a medium saucepan with one can of coconut milk and 1 cup water. Bring to a boil, then lower the heat, cover, and simmer for 15 minutes until the rice is tender. Remove from heat and let it sit covered.
Heat a large skillet over medium heat. Add the chicken and cook until lightly browned on all sides, about 5 minutes.
Stir in the onion and garlic. Cook for 3 minutes until the onion softens.
Add the green curry paste and cook for 1 minute until fragrant.
Pour in the second can of coconut milk, fish sauce, and sugar. Simmer for 10 minutes until the chicken is cooked through.
Stir in the spinach and cook just until it wilts, about 2 minutes. Squeeze in the lime juice from one wedge.
Fluff the rice and divide it among four bowls. Spoon the curry over the rice and top with cilantro and extra lime wedges.