Cut cilantro roots off at the stem, and mince thoroughly. Set aside a few leaves for garnish. In a blender or food processor, combine cilantro roots and leaves, garlic, chile peppers, turmeric, curry powder, sugar, and salt. Process to a coarse paste. Pour in fish sauce, and blend until smooth.
Place chicken in a large shallow dish. Rub with the cilantro paste. Cover, and marinate in the refrigerator at least 3 hours, or overnight.
Preheat grill for high heat.
Lightly oil the grill grate. Place chicken on the prepared grill, and brush liberally with coconut milk. Grill chicken 8 to 15 minutes on each side, depending on the size of the pieces. Turn only once, and baste occasionally with coconut cream. Cook until browned and tender, and juices run clear.