Human noroviruses (HuNoVs) circulate globally, affect all age groups and place a substantial burden upon health services. High genetic diversity leading to antigenic variation plays a significant role in HuNoV epidemiology, driving periodic global emergence of epidemic variants. Studies have suggested that immunocompromised individuals may be a reservoir for such epidemic variants, but studies investigating the diversity and emergence of HuNoV variants in immunocompetent individuals are underrepresented. To address this, we sequenced the genomes of HuNoVs present in samples collected longitudinally from one immunocompetent (acute infection) and one immunocompromised (chronic infection) patient. A broadly reactive HuNoV capture-based method was used to concentrate the virus present in these specimens prior to massively parallel sequencing to recover near complete viral genomes. Using a novel bioinformatics pipeline, we demonstrated that persistent minor alleles were present in both acute and chronic infections, and that minor allele frequencies represented a larger proportion of the population during chronic infection. In acute infection, minor alleles were more evenly spread across the genome, although present at much lower frequencies, and therefore difficult to discern from error. By contrast, in the chronic infection, more minor alleles were present in the minor structural protein. No non-synonymous minor alleles were detected in the major structural protein over the short sampling period of the HuNoV chronic infection, suggesting where immune pressure is variable or non-existent, epidemic variants could emerge over longer periods of infection by random chance.