You should not get a chemical peel during pregnancy.

More Info: According to the Johns Hopkins Cosmetic Center, pregnant women and those breastfeeding should not undergo a glycolic acid chemical peel.

(Glycolic Acid Peels: Johns Hopkins)

Embryo Growth

During pregnancy the embryo is developing in the womb protected by the maternal placenta barrier.  The placenta is highly effective at protecting the embryo, but it can react differently to different chemical structures.  As an example, those substances that are lipophilic, that is having the ability to dissolve in fat and oils, can penetrate the barrier.

Err on the Side of Caution

According to Dr Low Chai Ling in his book In Full Bloom: Look Fabulous During and After Pregnancy, mild peels such as those using alpha hydroxy acids (AHA) and trichloro acetic acid (TCA) are generally safe.  He does caution that beta hydroxy acids (BHA), such as salicylic acid, have not been tested on pregnant women and should therefore be avoided.

As the research is sparse, many doctors advise pregnant women to wait to have the procedure performed as a precautionary recommendation rather than one firmly rooted in scientific research.

Skin May React Differently

Another reason that you may want to avoid a chemical peel during pregnancy is that many pregnant women experience skin sensitivity.  Your skin may react very differently to a procedure that you may have previously undergone with little trouble.