While giant viruses (phylum Nucleocytoviricota) that infect protists have been studied for over two decades, the number of isolated systems remains limited to a few hosts, lagging behind the immense diversity inferred from environmental sequencing. The chlorarachniophyte alga Bigelowiella natans has been suggested as a potential host for giant viruses, but no isolates could thus far confirm this observation. Here, we present four closely related strains of giant viruses that infect B. natans and related algae, and therefore we designate them as chlorarachniophyte viruses (ChlorVs). We characterize their infection cycle and show that ChlorVs possess a large host range among chlorarachniophytes. The genomes of all strains were assembled using a combination of long and short reads, revealing linear topologies with terminal inverted repeats and sizes between 469 and 493 kbp. Phylogenetic analysis of marker genes using complex evolutionary models places the ChlorVs in the same subfamily as the Cafeteria roenbergensis virus (CroV) and the Chlorella virus XW01, indicating that switches between distantly related hosts are more common than previously known. ChlorVs share conserved promoter motifs for early and late genes with CroV, but completely lack the FNIP repeats that constitute ~60 kbp of the CroV genome. While all four genomes are highly similar and largely syntenic, they encode several strain-specific genes annotated as methyltransferases or helicases. This dynamic system provides unique insights into viral adaptations and virus genome evolution in a mixotrophic host.