The current document is directed to methods and systems that establish secure, verifiable chains of control for computational entities within a distributed computing system. When a computational entity is first instantiated or introduced into the distributed computing system, public and private identities are generated for the computational entity and secure control is established over the computational entity by an initial controlling entity. Subsequently, control of the computational entity may be transferred from the initial controlling entity to a different controlling entity using a secure, three-party transaction that records the transfer of control in a distributed public ledger. As control of the computational entity is subsequently transferred to different controlling entities by secure three-party transactions, a chain of control from one controlling entity to another is established and recorded in the distributed public ledger. The computational entity is controlled by a single controlling entity at each point in time from the first instantiation or introduction into the distributed computing system to termination or removal from the distributed computing system.