Like many double-stranded DNA viruses, tumor gammaherpesviruses Epstein-Barr virus and Kaposi's sarcoma-associated herpesvirus withstand high internal pressure. Bacteriophage HK97 uses covalent chainmail for this purpose, but how this is achieved noncovalently in the much larger gammaherpesvirus capsid is unknown. Our cryoelectron microscopy structure of a gammaherpesvirus capsid reveals a hierarchy of four levels of organization: (1) Within a hexon capsomer, each monomer of the major capsid protein (MCP), 1,378 amino acids and six domains, interacts with its neighboring MCPs at four sites. (2) Neighboring capsomers are linked in pairs by MCP dimerization domains and in groups of three by heterotrimeric triplex proteins. (3) Small (∼280 amino acids) HK97-like domains in MCP monomers alternate with triplex heterotrimers to form a belt that encircles each capsomer. (4) One hundred sixty-two belts concatenate to form noncovalent chainmail. The triplex heterotrimer orchestrates all four levels and likely drives maturation to an angular capsid that can withstand pressurization.