Special equipment: Ten 8-inch bamboo skewers, soaked in water 30 minutes
In a small bowl stir together coconut milk, soy sauce, curry powder, and ground coriander until combined well. Transfer 1/2 cup coconut mixture to a medium bowl and stir in cornstarch, reserving remaining coconut mixture, covered and chilled.
Cut chicken lengthwise into ten 1/2-inch-thick strips and add to cornstarch mixture, stirring to coat. Marinate chicken, covered and chilled, at least 1 hour and up to 24.
In a small saucepan stir together reserved coconut mixture, peanuts, lime juice, and red pepper flakes and simmer, stirring occasionally, 10 minutes, or until thickened. Transfer dipping sauce to a small bowl and cool.
Thread 1 piece chicken onto each skewer and grill on an oiled rack set 5 to 6 inches over glowing coals until cooked through, about 3 minutes on each side.
Sprinkle dipping sauce with fresh coriander and serve at room temperature with chicken sates.