Although the arrangement of internal organs in most metazoans is profoundly left-right (L/R) asymmetric with a predominant handedness, rare individuals show full (mirror-symmetric) or partial (heterotaxy) reversals. While the nematode Caenorhabditis elegans is known for its highly determinate development, including stereotyped L/R organ handedness, we found that L/R asymmetry of the major organs, the gut and gonad, varies among natural isolates of the species in both males and hermaphrodites. In hermaphrodites, heterotaxy can involve one or both bilaterally asymmetric gonad arms. Male heterotaxy is probably not attributable to relaxed selection in this hermaphroditic species, as it is also seen in gonochoristic Caenorhabditis species. Heterotaxy increases in many isolates at elevated temperature, with one showing a pregastrulation temperature-sensitive period, suggesting a very early embryonic or germline effect on this much later developmental outcome. A genome-wide association study of 100 isolates showed that male heterotaxy is associated with three genomic regions. Analysis of recombinant inbred lines suggests that a small number of loci are responsible for the observed variation. These findings reveal that heterotaxy is a widely varying quantitative trait in an animal with an otherwise highly stereotyped anatomy, demonstrating unexpected plasticity in an L/R arrangement of the major organs even in a simple animal.This article is part of the themed issue 'Provocative questions in left-right asymmetry'.