Make sauce: In a blender, combine peanut butter, chutney, lime juice, 1 tablespoon soy sauce, garlic, pepper flakes, 1/4 teaspoon salt, and 1/4 cup water; blend until smooth. Set aside.
Thread each chicken piece onto a skewer (fold the pieces slightly as you work so the skewers go in and out of the meat). Place skewered chicken in a shallow dish; season with salt and pepper. Drizzle oil and remaining tablespoon soy sauce over chicken; turn to coat.
Heat grill to high; lightly oil grates. Grill chicken until cooked through, about 3 minutes per side. Transfer to a platter; garnish with cilantro, if desired. Serve with chutney sauce.
The peanut-chutney sauce can be refrigerated in a covered container for up to a week. If you like, double the recipe, and serve the extra with grilled pork or as a dipping sauce for shrimp.