Cut each chicken breast lengthwise into six strips. Blend together all the ingredients for the marinade in a shallow dish. Add the chicken, turn several times to coat, then cover and marinate in the refrigerator for 2 hours or overnight.
Soak 24 wooden skewers in plenty of cold water for at least 30 minutes. Alternatively, use metal skewers.
To make the satay sauce, put the coconut in a jug, pour in 100ml of boiling water and leave to infuse for 15 minutes. Strain, reserving the coconut-flavoured liquid. Discard the coconut. Preheat a grill to a moderate heat.
Put all the ingredients for the satay sauce, including the coconut liquid, in a blender or food processor and whizz together. Transfer to a small serving bowl.
Thread each strip of chicken onto a skewer concertina-style, then grill for 10 minutes, or until cooked through. (Alternatively, cook the skewers on a chargrill pan.) Serve the chicken skewers with the satay sauce. Offer lime or lemon wedges to squeeze over.