Present workflows for producing human genome assemblies from long-read technologies have cost and production time bottlenecks that prohibit efficient scaling to large cohorts. We demonstrate an optimized PromethION nanopore sequencing method for eleven human genomes. The sequencing, performed on one machine in nine days, achieved an average 63x coverage, 42 Kb read N50, 90% median read identity and 6.5x coverage in 100 Kb+ reads using just three flow cells per sample. To assemble these data we introduce new computational tools: Shasta – a de novo long read assembler, and MarginPolish & HELEN – a suite of nanopore assembly polishing algorithms. On a single commercial compute node Shasta can produce a complete human genome assembly in under six hours, and MarginPolish & HELEN can polish the result in just over a day, achieving 99.9% identity (QV30) for haploid samples from nanopore reads alone. We evaluate assembly performance for diploid, haploid and trio-binned human samples in terms of accuracy, cost, and time and demonstrate improvements relative to current state-of-the-art methods in all areas. We further show that addition of proximity ligation (Hi-C) sequencing yields near chromosome-level scaffolds for all eleven genomes.