Giardia lamblia is medically important as a cause of diarrhea and malabsorption throughout the world and is thought to be one of the earliest-branching eukaryotes on a phylogenetic tree. Nevertheless, the mechanisms of inheritance are largely unknown. The trophozoites of Giardia and other diplomonads are interesting in their possession of two nuclei that are identical or similar in several respects. They replicate at nearly the same time, have similar quantities of DNA, and are both transcriptionally active. We used fluorescence in situ hybridization to demonstrate that genes from each of the five chromosomes are found in both nuclei, confirming that each nucleus has at least one complete copy of the genome. This raises a second question. The alleles of a gene in different nuclei are expected to accumulate different mutations, but surprisingly, the degree of heterozygosity in a clone is very low. One possible mechanism for eliminating sequence differences between nuclei is that each daughter cell receives two copies of the same nucleus at cell division. We used trophozoites with a plasmid transfected into a single nucleus to demonstrate that the two nuclei are partitioned equationally at cytokinesis. The mechanism(s) by which homozygosity is maintained will require further investigation.