In a medium bowl, stir together chicken, lime juice, brown sugar, ginger, salt, garlic and turmeric; cover and refrigerate for 30 min. Thread 1 piece of chicken onto each skewer.
Meanwhile, in a small saucepan over medium heat, stir together peanut butter, coconut milk, lime zest, lime juice, soy sauce, brown sugar, ginger and hot pepper flakes. Stir continuously until sauce is smooth and thickened, about 5 min.
Preheat lightly oiled grill to medium-high. Place skewers on grill; close lid and grill until cooked through, 4 to 5 min. per side. Serve with peanut sauce alongside for dipping.
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