An analysis of gene expression variability can provide an insightful window into how regulatory control is distributed across the transcriptome. In a single cell analysis, the inter-cellular variability of gene expression measures the consistency of transcript copy numbers observed between cells in the same population. Application of these ideas to the study of early human embryonic development may reveal important insights into the transcriptional programs controlling this process, based on which components are most tightly regulated. Using a published single cell RNA-seq data set of human embryos collected at four-cell, eight-cell, morula and blastocyst stages, we identified genes with the most stable, invariant expression across all four developmental stages. Stably-expressed genes were found to be enriched for those sharing indispensable features, including essentiality, haploinsufficiency, and ubiquitous expression. The stable genes were less likely to be associated with loss-of-function variant genes or human recessive disease genes affected by a DNA copy number variant deletion, suggesting that stable genes have a functional impact on the regulation of some of the basic cellular processes. Genes with low expression variability at early stages of development are involved in regulation of DNA methylation, responses to hypoxia and telomerase activity, whereas by the blastocyst stage, low-variability genes are enriched for metabolic processes as well as telomerase signaling. Based on changes in expression variability, we identified a putative set of gene expression markers of morulae and blastocyst stages. Experimental validation of a blastocyst-expressed variability marker demonstrated that HDDC2 plays a role in the maintenance of pluripotency in human ES and iPS cells. Collectively our analyses identified new regulators involved in human embryonic development that would have otherwise been missed using methods that focus on assessment of the average expression levels; in doing so, we highlight the value of studying expression variability for single cell RNA-seq data. In order to function properly, cells express specific sets of genes that are regulated via complex transcriptional programs. During early stages of development, when an embryo consists of only a handful of cells, it is vital that these cells work together so that the embryo can develop into a healthy baby. Single cell studies allow us to understand how each cell contributes to ensuring proper regulation of the embryo, as well as identify the critical genes whose expression is important for development. While we understand that regulation of a gene occurs through the timing of when it is expressed and also the quantity of its expression, more recently we have come to recognize that the variability of a gene’s expression across single cells may also contribute to the viability of the organism. In this study, we analyzed the gene expression variability of human embryos at different developmental stages. We discovered distinctive patterns of variability across cells in the embryo; some genes had extremely stable expression, and others were variable but with increased homogeneity in expression at a particular developmental stage. We validated one of these stage-specific markers and found that it played a role in the maintenance of pluripotency of human pluripotent stem cells. Overall, these results can help unlock additional clues into understanding how embryonic development is regulated in humans.