When is record-keeping better arranged through a blockchain 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 record-keeper extracts rents due to its monopoly on the ledger. Its franchise value dynamically incentivizes correct reporting. Blockchains drive down rents by allowing for free entry of  record-keepers and portability of information to competing ``forks.'' Blockchains must therefore provide static incentives for correctness through computationally expensive proof-of-work algorithms and permit record-keepers to roll back history in order to undo fraudulent reports. While blockchains can keep track of ownership transfers, enforcement of possession rights is often better complemented by centralized record-keeping.