Rinse chicken well and pat dry. Season with salt and pepper to taste.
In a food processor, or with a mortar and pestle, combine coriander, ginger, and garlic. Pulse a few times or mash to a coarse paste.
In a bowl, combine paste, coconut milk, fish sauce and lime juice. Stir until blended.
In a resealable bag, combine chicken and marinade. Marinate in the refrigerator for at least 4 hours or overnight. Drain chicken from marinade, discarding liquid.
Lightly oil grill grates and arrange chicken in a single layer on hot grates. Over hot coals, grill chicken for about 5 to 7 minutes and then turn to grill the other side for another 5 to 7 minutes or until a thermometer inserted reads 165 F.
Remove from heat and allow to rest for about 3 to 5 minutes before slicing.