Whole genome amplification by the multiple displacement amplification (MDA) method allows sequencing of genomes from single cells of bacteria that cannot be cultured. However, genome assembly is challenging because of highly non-uniform read coverage generated by MDA. We describe an improved assembly approach tailored for single cell Illumina sequences that incorporates a progressively increasing coverage cutoff. This allows variable coverage datasets to be utilized effectively with assembly of E. coli and S. aureus single cell reads capturing >91% of genes within contigs, approaching the 95% captured from a multi-cell E. coli assembly. We apply this method to assemble a single cell genome of the uncultivated SAR324 clade of Deltaproteobacteria, a cosmopolitan bacterial lineage in the global ocean. Metabolic reconstruction suggests that SAR324 is aerobic, motile and chemotaxic. These new methods enable acquisition of genome assemblies for individual uncultivated bacteria, providing cell-specific genetic information absent from metagenomic studies.