A large number of distinct HIV-1 genomes can be present in a single clinical sample from a patient chronically infected with HIV-1. We examined samples containing complex mixtures of near-full-length HIV-1 genomes. Single molecules were sequenced as near-full-length (9.6 kb) amplicons directly from PCR products without shearing. Mathematical analysis techniques deconvolved the complex mixture of reads into estimates of distinct near-full-length viral genomes with their relative abundances. We correctly estimated the originating genomes to single-base resolution along with their relative abundances for mixtures where the truth was known exactly by independent sequencing methods. Correct estimates were made even when genomes diverged by a single base. Minor abundances of 5% were reliably detected. SMRT Sequencing data contained near-full-length continuous reads for each sample including some runs with greater than 10,000 near-full-length-genome reads in a three-hour collection time. SMRT Sequencing yields long- read sequencing results from individual DNA molecules with a rapid time-to-result. The single-molecule, full-length nature of the sequencing method allows us to estimate variant subspecies and relative abundances even from samples containing complex mixtures of genomes that differ by single bases. These results open the possibility of cost-effective full-genome sequencing of HIV-1 in mixed populations for applications such as incorporated-HIV-1 screening. In screening, genomes can differ by one to many thousands of bases and the ability to measure them can help scientifically inform treatment strategies.