Chemical peels can work wonderfully around the eyes, especially under them, to improve fine lines, wrinkles, and sun damage. However, the strength of the peel (which determines the depth of the peel) is very important to achieve effectiveness. Very light and light peels will help with pigment and texture, but won't do much to help with fine lines and wrinkles, no matter how often they are repeated. For improving fine lines and wrinkles you need a medium depth peel. My favorite is the Monheit combination peel, which consists of application of Jessner's solution and 35% TCA. You will have about a one week downtime, but this level is necessary to really achieve improvement.
Be sure to see someone who has extensive experience in chemical peeling, and make sure they show you before, during and after pictures of patients that they've treated before. The eyelid skin is the thinnest skin of the face, and cautious, safe peeling can help you achieve wonderful results. Of note, a hyaluronic acid filler such as Juvederm, may also improve the area under the eye, and these procedures can be combined.