Efficient checkpointing and resumption of multicomputer applications is essential if multicomputers are to support time-sharing and the automatic resumption of jobs after a system failure. We present a checkpointing scheme that is transparent, imposes overhead only during checkpoints, requires minimal message logging, and allows for quick resumption of execution from a checkpointed image. Since checkpointing multicomputer applications poses requirements different from those posed by checkpointing general distributed systems, existing distributed checkpointing schemes are inadequate for multicomputer checkpointing. Our checkpointing scheme makes use of special properties of multicomputer interconnection networks to satisfy this new set of requirements.