Fault tolerance of a blockchain is often characterized by the fraction f of "adversarial power" that it can tolerate in the system. Despite the fast progress in blockchain designs in recent years, existing blockchain systems can still only tolerate f below 1 2 . Can practically usable blockchains tolerate a malicious majority, i.e., f ≥ 1 2 ? This work presents a positive answer to this question. We first note that the well-known impossibility of byzantine consensus under f ≥ 1 2 does not carry over to blockchains. To tolerate f ≥ 1 2 , we use byzantine broadcast, instead of byzantine consensus, as the core of the blockchain. A major obstacle in doing so, however, is that the resulting blockchain may have extremely low throughput. To overcome this central technical challenge, we propose a novel byzantine broadcast protocol OVERLAYBB, that can tolerate f ≥ 1 2 while achieving good throughput. Using OVERLAYBB as the core, we present the design, implementation, and evaluation of a novel Proof-of-Stake blockchain called BCUBE. BCUBE can tolerate a malicious majority, while achieving practically usable transaction throughput and confirmation latency in our experiments with 10000 nodes and under f = 0.7. To our knowledge, BCUBE is the first blockchain that can achieve such properties.1 A similar requirement has led to the recent impossibility result in [10].