In a glass bowl, mix chicken breast cubes with lime juice, lime zest, and grated ginger. Let marinate for about 20 minutes.
In a medium saucepan, combine the coconut milk and sugar over medium-high heat. Bring to a simmer. Stir in the jasmine rice, reduce heat to low, and cook tightly covered for about 20 minutes or until liquid is absorbed. Remove from the heat and fluff rice with a fork; cover, and keep warm.
In a large skillet or wok, heat the sesame oil over medium-high heat. Add chicken and marinade. Stir fry until the chicken is nicely browned, about 3 minutes. Drizzle the honey onto the chicken and continue to stir-fry for another minute or so, being careful not to let the honey burn. Remove from the heat and sprinkle with coconut.