Haplotypes are fundamental to fully characterize the diploid genome of an individual, yet methods to directly chart the unique genetic makeup of each parental chromosome are lacking. Here we introduce single-cell DNA template strand sequencing (Strand-seq) as a novel approach to phasing diploid genomes along the entire length of all chromosomes. We demonstrate this by building a complete haplotype for a HapMap individual (NA12878) at high accuracy (concordance 99.3%), without using generational information or statistical inference. By use of this approach, we mapped all meiotic recombination events in a family trio with high resolution (median range ∼14 kb) and phased larger structural variants like deletions, indels, and balanced rearrangements like inversions. Lastly, the single-cell resolution of Strand-seq allowed us to observe loss of heterozygosity regions in a small number of cells, a significant advantage for studies of heterogeneous cell populations, such as cancer cells. We conclude that Strand-seq is a unique and powerful approach to completely phase individual genomes and map inheritance patterns in families, while preserving haplotype differences between single cells.