Bitcoin is the most secure blockchain in the world, supported by the immense hash power of its Proof-of-Work miners. Proof-of-Stake chains are energy-efficient, have fast finality but face several security issues: susceptibility to non-slashable long-range safety attacks, low liveness resilience and difficulty to bootstrap from low token valuation. We show that these security issues are inherent in any PoS chain without an external trusted source, and propose a new protocol, Babylon, where an off-the-shelf PoS protocol checkpoints onto Bitcoin to resolve these issues. An impossibility result justifies the optimality of Babylon. A use case of Babylon is to reduce the stake withdrawal delay: our experimental results show that this delay can be reduced from weeks in existing PoS chains to less than 5 hours using Babylon, at a transaction cost of less than 10K USD per annum for posting the checkpoints onto Bitcoin.