This paper proposes a solution to the problem of browser-based fingerprinting. An important observation is that making fingerprints non-deterministic also makes them hard to link across subsequent web site visits. Our key insight is that when it comes to web tracking, the real problem with fingerprinting is not uniqueness of a fingerprint, it is linkability, i.e. the ability to connect the same fingerprint across multiple visits. In PriVaricator we use the power of randomization to "break" linkability by exploring a space of parameterized randomization policies. We evaluate our techniques in terms of being able to prevent fingerprinting and also in terms of not breaking existing (benign) sites. The best of our randomization policies renders all the fingerprinters we tested ineffective, while causing minimal damage on a set of 1,000 Alexa sites on which we tested, with no noticeable performance overhead.