Is the chickenpox vaccine safe for adults to get?

Yes. Adults are prone to worse complications from the disease than children.
Chickenpox vaccine. Varicella (chickenpox) vaccine is very safe. The current generation is immune to chickenpox because each have had 2 doses of the vaccine. Unvaccinated couples planning a family are advised to get immunized with the vaccine before starting pregnancy to insure the baby's safety. Chickenpox acquired by a newborn baby can be fatal.