Previous studies have linked the evolution of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) genetic variants to persistent infections in people with immunocompromising conditions, but the processes responsible for these observations are incompletely understood. Here we use high-throughput, single-genome amplification and sequencing (HT-SGS) to sequence SARS-CoV-2 spike genes from people with HIV (PWH, n = 22) and people without HIV (PWOH, n = 25). In PWOH and PWH with CD4 T cell counts (i.e., CD4 counts) ≥ 200 cells/μL, we find that most SARS-CoV-2 genomes sampled in each person share one spike sequence. By contrast, in people with advanced HIV infection (i.e., CD4 counts < 200 cells/μL), HT-SGS reveals a median of 46 distinct linked groupings of spike mutations per person. Elevated intra-host spike diversity in people with advanced HIV infection is detected immediately after COVID-19 symptom onset, and early intra-host spike diversity predicts SARS-CoV-2 shedding duration among PWH. Analysis of longitudinal timepoints reveals rapid fluctuations in spike sequence populations, replacement of founder sequences by groups of new haplotypes, and positive selection at functionally important residues. These findings demonstrate remarkable intra-host genetic diversity of SARS-CoV-2 in advanced HIV infection and suggest that adaptive intra-host SARS-CoV-2 evolution in this setting may contribute to the emergence of new variants of concern.