Can I use a chemical peel under my eyes?

Chemical peels an excellent way to tighten and smooth the skin under the eyes without invasive measures such as blepharoplasty.  In general, surgery is reserved for removing excess fat or an abundance of redundant skin.  If you have fine wrinkles then chemical peels (Glycolic or TCA) or laser (CO2RE fractioned CO2) or radio frequency (Sublative) with or without Botox to help with dynamic lines are excellent treatments.  Chemical peels should NOT be performed at home or from some product you order on the internet.  Peels, just like laser and other treatments, should be performed in your doctor's office by experienced and trained practitioners.  Good luck

The Perfect Derma Peel is an advanced effective medical grade peel and can be used on the eye lids as well as under the eyes. It consists of TCA. Retinoic, Salicylic and Kojic acid and helps with fine lines under the eyes and discoloration.  Radio frequency is another good alternative for tightening under the eyes and reducing fine lines.

From your question it appears you are preparing to apply acid under your eyes and I think you would do better to see a health care professional. even though 20%  glycolic acid is not very strong it would be a very bad scenario if it got in your eyes. I developed the glycolic acid system for MD Formulations and aestheticians have a weak form and doctors a stronger one