Soak dried chilies in water overnight or until soft; remove seeds. Place ingredients, except meat, in a food processor; process until smooth. Spread mixture over the chicken; refrigerate at least 1 hour, up to 24 hours.
Heat grill to 400 degrees, or if cooking inside, heat a small amount of oil in a skillet or grill pan over high heat. Season chicken with salt. Grill chicken breasts until cooked through.