Trim excess skin and fat from chicken. In a 12-inch skillet cook chicken, skin side down, in hot olive oil for 8 minutes, or until browned. (Do not turn thighs). Remove from heat; drain and discard fat.
In a slow cooker combine carrots and onion. In a bowl, whisk together half of the coconut milk and the curry paste; pour over carrots and onion (refrigerate remaining coconut milk). Place chicken, skin side up, on vegetables. Cook on HIGH for 3 1/2 to 4 hours, or on LOW for 7 to 8 hours.
Remove chicken to platter. Skim off excess fat, then stir in remaining coconut milk. Top each serving with your choice of pistachios, raisins, cilantro, and/or crushed red pepper flakes. Enjoy!