The epigenetic DNA modification 5-hydroxymethylcytosine (5hmC) has crucial roles in development and gene regulation. Quantifying the abundance of this epigenetic mark at the single-cell level could enable us to understand its roles. We present a single-cell, genome-wide and strand-specific 5hmC sequencing technology, based on 5hmC glucosylation and glucosylation-dependent digestion of DNA, that reveals pronounced cell-to-cell variability in the abundance of 5hmC on the two DNA strands of a given chromosome. We develop a mathematical model that reproduces the strand bias and use this model to make two predictions. First, the variation in strand bias should decrease when 5hmC turnover increases. Second, the strand bias of two sister cells should be strongly anti-correlated. We validate these predictions experimentally, and use our model to reconstruct lineages of two- and four-cell mouse embryos, showing that single-cell 5hmC sequencing can be used as a lineage reconstruction tool.