Latency is a common strategy in a wide range of viral lineages, but its prevalence in giant viruses remains unknown. Here we describe a 617 kbp integrated giant viral element in the model green alga Chlamydomonas reinhardtii. We resolve the integrated viral genome using long-read sequencing, identify a putative polinton-like integrase, and show that viral particles accumulate primarily during the stationary growth phase. A diverse array of viral-encoded selfish genetic elements is expressed during viral activity, including several Fanzor nuclease-encoding transposable elements. In addition, we show that field isolates of Chlamydomonas sp. harbor signatures of endogenous giant viruses related to the C. reinhardtii virus that exhibit similar infection dynamics, suggesting that giant virus latency is prevalent in natural host communities. Our work describes an unusually large temperate virus of a unicellular eukaryote, substantially expanding the scope of cryptic viral infections in the virosphere.