Tardigrades are microscopic animals that can survive exceptional levels of ionizing radiation or desiccation-DNA-damaging conditions that would kill most animals. Irradiation or radiomimetic drug treatment of the tardigrade Hypsibius exemplaris can induce remarkably high expression levels of DNA repair genes, primarily those in the base excision repair and nonhomologous end joining pathways. How tardigrades can repair widespread DNA damage without producing frequent, large-scale chromosome structural abnormalities, like chromosome translocations and fusions, is unknown. Here, we report the results of examining chromosome and nuclear architecture throughout the cell cycle in early embryos of H. exemplaris. We found that H. exemplaris chromosomes are maintained in an individualized form throughout the cell cycle. We were surprised to also find that each chromosome is housed in a fully or partially separate lamin-lined compartment, instead of all chromosomes being housed in a single, nearly spherical nuclear lamina and envelope. Our results reveal unusual chromosomal and nuclear organization in a tardigrade. We speculate that these unexpected features might limit chromosomal rearrangements during DNA damage repair in extreme conditions.