Genome sequencing of large numbers of individuals promises to advance the understanding, treatment, and prevention of human diseases, among other applications. We describe a genome sequencing platform that achieves efficient imaging and low reagent consumption with combinatorial probe anchor ligation chemistry to independently assay each base from patterned nanoarrays of self-assembling DNA nanoballs. We sequenced three human genomes with this platform, generating an average of 45- to 87-fold coverage per genome and identifying 3.2 to 4.5 million sequence variants per genome. Validation of one genome data set demonstrates a sequence accuracy of about 1 false variant per 100 kilobases. The high accuracy, affordable cost of $4400 for sequencing consumables, and scalability of this platform enable complete human genome sequencing for the detection of rare variants in large-scale genetic studies.