Genome sequencing of single cells has a variety of applications, including characterizing difficult-to-culture microorganisms and identifying somatic mutations in single cells from mammalian tissues. A major hurdle in this process is the bias in amplifying the genetic material from a single cell, a procedure known as polymerase cloning. Here we describe the microwell displacement amplification system (MIDAS), a massively parallel polymerase cloning method in which single cells are randomly distributed into hundreds to thousands of nanoliter wells and their genetic material is simultaneously amplified for shotgun sequencing. MIDAS reduces amplification bias because polymerase cloning occurs in physically separated, nanoliter-scale reactors, facilitating the de novo assembly of near-complete microbial genomes from single Escherichia coli cells. In addition, MIDAS allowed us to detect single-copy number changes in primary human adult neurons at 1- to 2-Mb resolution. MIDAS can potentially further the characterization of genomic diversity in many heterogeneous cell populations.