Do chemical peels work for deep vertical lines around the mouth?

Unless you are doing a very strong TCA or phenol peel, the best alternative for you is co2 laser resurfacing with or without fillers.  I suggest seeing a well trained dermatologist for this, someone with a lot of experience in lasers and peels.  Best, Dr. Emer.

Phenol 89% or Baker Gordon Phenol are the agents of choice for this provided you have the right complexion.  These agents also damage melanin in the skin and can make the peeled skin hypopigmented.  By careful patient selection, these agents are best for fairly lightly complexed individuals.  A personal consultation is needed to assess this for you.