The first lineage specification of pluripotent mouse epiblast segregates neuroectoderm (NE) from mesoderm and definitive endoderm (ME) by mechanisms that are not well understood. Here we demonstrate that the induction of ME gene programs critically relies on the T-box transcription factors Eomesodermin (also known as Eomes) and Brachyury, which concomitantly repress pluripotency and NE gene programs. Cells deficient in these T-box transcription factors retain pluripotency and differentiate to NE lineages despite the presence of ME-inducing signals transforming growth factor β (TGF-β)/Nodal and Wnt. Pluripotency and NE gene networks are additionally repressed by ME factors downstream of T-box factor induction, demonstrating a redundancy in program regulation to safeguard mutually exclusive lineage specification. Analyses of chromatin revealed that accessibility of ME enhancers depends on T-box factor binding, whereas NE enhancers are accessible and already activation primed at pluripotency. This asymmetry of the chromatin landscape thus explains the default differentiation of pluripotent cells to NE in the absence of ME induction that depends on activating and repressive functions of Eomes and Brachyury.