A number of applications from smartcard to ePassport to eID depend on preventing unauthorized access to hardware and software functionality. Physically Unclonable Functions (PUF) rely on manufacturing process variations to create unique identifiers that can be used for various security applications including authentication and secure access. For practical applications, PUFs are required to be unique for each chip. Such property cannot be ensured by design alone. Since PUFs rely on manufacturing process variations, there are no guarantees that two PUFs will never have identical properties. Therefore, testing becomes necessary to screen out PUFs that violate the above property. Despite decades of research on PUFs, there has been scant attention to the problem of testing PUFs for uniqueness. In this paper, we investigate the problem of testing PUFs for uniqueness and we propose techniques for Uniqueness testing. The proposed methods are low-cost and are tailored for testing PUFs using hardware testers.