Blockchain technology holds the promise of transforming our financial system but a key question lingers regarding whether this technology can ensure secure settlement. We develop an equilibrium model to study that question with regard to the most prominent blockchain type, a Proof-of-Stake (PoS) blockchain. We demonstrate that blockchain security increases with the productivity of the blockchain. Moreover, we show that there exist reasonable conditions under which a PoS blockchain is secure against arbitrarily large incentives to disrupt settlement.