Using a large mortar & pestle or a small food processor, combine the garlic, salt/pepper & pound or process to a smooth paste. Add the coriander root & pound or process to a paste. Transfer to a large bowl & stir in the fish sauce & coconut milk (shake the tin vigorously prior to adding or break up the solid packaged coconut milk into small pieces, melt slightly to turn into a liquid).
Slice the chicken breasts into 8 smaller pieces (slice chicken breast in half and then slice each half into 4 pieces).
Place the chicken in the marinade & stir to coat well. Marinate in the fridge overnight or if you are eating immediately, allow chicken to marinate for 1 hour 60 Minutes at room temperature.
To cook your chicken you can either grill on your barbeque or broil in your oven. Grill one side 1st and then turn over and brush with marinade as you cook! Chicken is ready once juices run clear when sliced. Enjoy your taste of Thai.