In a baking dish, soak bamboo skewers in water, for at least one hour. Reserve.
Heat oil in small skillet over medium heat, until fragrant and lightly browned, about 1 minute. Cool.
In a large bowl, combine coconut milk, fish sauce, brown sugar, curry paste, cilantro, salt, and cooled garlic and any remaining oil. Add chicken and toss to coat. Refrigerate up to 4 hours. Thread chicken onto soaked skewers. Lightly grease grill or grill pan. Cook, turning once, for 5-7 minutes or until no longer pink inside and cooked through.