Heat-shock proteins (HSPs) are ubiquitous proteins with important roles in response to biotic and abiotic stress. The 70-kDa heat-shock genes (Hsp70s) encode a group of conserved chaperone proteins that play central roles in cellular networks of molecular chaperones and folding catalysts across all the studied organisms including bacteria, plants and animals. Several Hsp70s involved in drought tolerance have been well characterized in various plants, whereas no research on Chenopodium quinoa HSPs has been completed. Here, we analyzed the genome of C. quinoa and identified sixteen Hsp70 members in quinoa genome. Phylogenetic analysis revealed the independent origination of those Hsp70 members, with eight paralogous pairs comprising the Hsp70 family in quinoa. While the gene structure and motif analysis showed high conservation of those paralogous pairs, the synteny analysis of those paralogous pairs provided evidence for expansion coming from the polyploidy event. With several subcellular localization signals detected in CqHSP70 protein paralogous pairs, some of the paralogous proteins lost the localization information, indicating the diversity of both subcellular localizations and potential functionalities of those HSP70s. Further gene expression analyses revealed by quantitative polymerase chain reaction (qPCR) analysis illustrated the significant variations of Cqhsp70s in response to drought stress. In conclusion, the sixteen Cqhsp70s undergo lineage-specific expansions and might play important and varied roles in response to drought stress.