Best to try a concealer first

Most chemical peels will not correct the very dark circles under the eyes. Some of the conditions that lead to dark circles are the thinness of the skin coupled with multiple blood vessels below the skin. Also if there are bags of the lower eyelids this casts a shadow and will accentuate the deepness and the darkness of the area. In my experience chemical peeling is not of much benefit and can also cause a darkening of the skin. Try to use products that conceal the darkness. One such product is Teamine Eye Complex. I hope that this helps.