Designing a secure permissionless distributed ledger (blockchain) that performs on par with centralized payment processors, such as Visa, is a challenging task. Most existing distributed ledgers are unable to scale-out, i.e., to grow their total processing capacity with the number of validators; and those that do, compromise security or decentralization. We present OmniLedger, a novel scale-out distributed ledger that preserves longterm security under permissionless operation. It ensures security and correctness by using a bias-resistant public-randomness protocol for choosing large, statistically representative shards that process transactions, and by introducing an efficient crossshard commit protocol that atomically handles transactions affecting multiple shards. OmniLedger also optimizes performance via parallel intra-shard transaction processing, ledger pruning via collectively-signed state blocks, and low-latency “trust-butverify” validation for low-value transactions. An evaluation of our experimental prototype shows that OmniLedger’s throughput scales linearly in the number of active validators, supporting Visa-level workloads and beyond, while confirming typical transactions in under two seconds.