While neural crest development is known to be transcriptionally controlled via sequential activation of gene regulatory networks (GRNs), recent evidence increasingly implicates a role for post-transcriptional regulation in modulating the output of these regulatory circuits. Using available single-cell RNA-sequencing datasets from avian embryos to identify potential post-transcriptional regulators, we found that Elavl1, which encodes for an RNA-binding protein with roles in transcript stability, was enriched in the premigratory cranial neural crest. Perturbation of Elavl1 resulted in premature neural crest delamination from the neural tube as well as significant reduction in transcripts associated with the neural crest specification GRN, phenotypes that are also observed with downregulation of the canonical Wnt inhibitor Draxin. That Draxin is the primary target for stabilization by Elavl1 during cranial neural crest specification was shown by RNA-sequencing, RNA immunoprecipitation, RNA decay measurement, and proximity ligation assays, further supporting the idea that the downregulation of neural crest specifier expression upon Elavl1 knockdown was largely due to loss of Draxin. Importantly, exogenous Draxin rescued cranial neural crest specification defects observed with Elavl1 knockdown. Thus, Elavl1 plays a critical a role in the maintenance of cranial neural crest specification via Draxin mRNA stabilization. Together, these data highlight an important intersection of post-transcriptional regulation with modulation of the neural crest specification GRN.