Embryonic development relies on the capacity of progenitor cells to appropriately respond to inductive cues, a cellular property known as developmental competence. Here, we report that epigenetic priming of enhancers signifies developmental competence during endodermal lineage diversification. Chromatin mapping during pancreatic and hepatic differentiation of human embryonic stem cells revealed the en masse acquisition of a poised chromatin state at enhancers specific to endoderm-derived cell lineages in gut tube intermediates. Experimentally, the acquisition of this poised enhancer state predicts the ability of endodermal intermediates to respond to inductive signals. Furthermore, these enhancers are first recognized by the pioneer transcription factors FOXA1 and FOXA2 when competence is acquired, while subsequent recruitment of lineage-inductive transcription factors, such as PDX1, leads to enhancer and target gene activation. Together, our results identify the acquisition of a poised chromatin state at enhancers as a mechanism by which progenitor cells acquire developmental competence.