Can a chemical peel under the eyes near the lashes remove fine lines? And is it a good idea?

It is an option. In a chemical peel, a chemical solution is applied to the skin and allowed to soak in. Over the next 1 to 14 days, depending on how deeply the chemical penetrated the skin, the skin peels off. This procedure destroys parts of the skin in a controlled way so that new skin can grow in its place. Types of chemical peels differ based on how deeply the chemical penetrates and what type of chemicals use.