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 $0.5$. Can practically usable blockchains tolerate a malicious majority, i.e., $f$ above $0.5$? This work presents a positive answer to this question. We first note that the well-known impossibility of {\em byzantine consensus} for $f$ above $0.5$ does not carry over to blockchains. To tolerate $f$ above $0.5$, we use {\em 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 $f$ above $0.5$ 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.