I am replacing a power cord that is too short for the chandelier. It has a ground wire but do I really need one.

Yes, a ground wire is needed to insure that any exposed metal on a light fixture is grounded.

A short circuit in a light fixture can easily energize any metal frame. A person can come along and touch the metal frame, and if they are grounded, will complete the circuit and receive a shock, at best, and worse, the shock may be fatal.

Thank you