In a mixing bowl, whisk together olive oil, lime juice, soy sauce, honey, ginger, garlic, salt, and pepper. Place the chicken breasts in a large ziplock bag or a shallow dish. Pour the marinade over the chicken, ensuring each piece is well coated. Seal or cover, and refrigerate for at least 2 hours, or overnight for best results.
Preheat your grill or grill pan to medium-high heat. Remove the chicken from the marinade, letting any excess drip off.
Grill the chicken for 6-8 minutes on each side, or until fully cooked through and charred on the outside. The internal temperature should reach 165°F. Rinse the jasmine rice under cold water until the water runs clear. In a medium saucepan, combine rinsed rice, coconut milk, water, sugar,and salt. Bring to a boil.
Once boiling, reduce the heat to low, cover, and simmer for 18-20 minutes, or until the liquid is absorbed and the rice is tender. Remove from heat and let it sit, covered, for 5 minutes. Fluff with a fork before serving.