Bacteria encode myriad defences that target the genomes of infecting bacteriophage, including restriction-modification and CRISPR-Cas systems . In response, one family of large bacteriophages uses a nucleus-like compartment to protect its replicating genomes by excluding host defence factors . However, the principal composition and structure of this compartment remain unknown. Here we find that the bacteriophage nuclear shell assembles primarily from one protein, which we name chimallin (ChmA). Combining cryo-electron tomography of nuclear shells in bacteriophage-infected cells and cryo-electron microscopy of a minimal chimallin compartment in vitro, we show that chimallin self-assembles as a flexible sheet into closed micrometre-scale compartments. The architecture and assembly dynamics of the chimallin shell suggest mechanisms for its nucleation and growth, and its role as a scaffold for phage-encoded factors mediating macromolecular transport, cytoskeletal interactions, and viral maturation.