1. Combine sugar, soy sauce, lemon juice, oil, garlic, and ginger in a small saucepan. Combine water with arrowroot in a small bowl and stir until arrowroot is dissolved. Add to saucepan and turn heat to high. Stir often while bringing mixture to a boil, then reduce heat and simmer for 4 to 6 minutes or until sauce is thick.
2. Preheat your grill on high for the chicken.
3. When the grill is hot, rub each chicken piece with oil and cook the chicken for 4 to 6 minutes per side or until completely cooked. Chicken should have browned in spots.
4. When chicken is done, chop it into bite-size pieces. Pour the chicken pieces into a large frying pan over medium heat. Heat until chicken sizzles then reduce heat and cover chicken until ready to serve. Spoon chicken into a medium bowl, then pour all the sauce over the chicken and stir until well coated.