When is record-keeping better arranged through distributed ledger technology (DLT) than through a traditional centralized intermediary? The ideal qualities of any record-keeping system are (i) correctness, (ii) decentralization, and (iii) cost efficiency. We point out a \textit{Blockchain Trilemma}: no ledger can satisfy all three properties simultaneously. A centralized ledger writer extracts rents due to its monopoly on the ledger. Its franchise value dynamically incentivizes honest reporting. Decentralized ledgers provide static incentives for honesty through computationally expensive Proof-of-Work algorithms but eliminate rents through “fork competition.” Portability of information between “forks” and competition among miners fosters competition among decentralized ledgers that is fiercer than traditional competition. However, fork competition can engender instability and miscoordination. While blockchains can keep track of ownership transfers, enforcement of possession rights is still needed in many blockchain applications.