In this paper, we present offchain runtime verification, a dynamic analysis technique to inspect blockchain executions without affecting the blockchain itself. Runtime verification (RV) is a technique that analyzes traces of system execution based on monitors created from system specifications. There are two flavors of RV: online and offline. In online RV, monitors run in tandem with the system, either with their own resources or as code inlined in the system implementation. In offline RV, monitors have a dump of the system trace available. Examples of offline monitoring include post-mortem analysis and log inspection. We present a novel notion of monitors running offchain while fetching information about the blockchain evolution and its agents (e.g. external users, bakers) to assess security and fairness, assign blame, and compute explanations. Our monitoring infrastructure is both online—as the monitors can receive new blocks incrementally—and offline since the monitors can query the history of the blockchain. Online queries are necessary because monitors are created after the blockchain has been running and relevant information is discovered online (e.g. who interacted in the past with an address recently discovered to be malicious). We describe in this paper an RV infrastructure for offchain monitoring for the Tezos Blockchain.