Herpesviruses are ubiquitous pathogens in need of novel therapeutic solutions. Current engineered gene drive strategies rely on sexual reproduction, and are thought to be restricted to sexual organisms. Here, we report on the design of a novel gene drive system that allows the spread of an engineered trait in populations of DNA viruses and, in particular, herpesviruses. We describe the successful transmission of a gene drive sequence between distinct strains of human cytomegalovirus (human herpesvirus 5) and show that gene drive viruses can efficiently target and replace wildtype populations in cell culture experiments. Our results indicate that viral gene drives can be used to suppress a viral infection and may represent a novel therapeutic strategy against herpesviruses.