At TN ≃ 300K the layered insulator BaCoS2 transitions to a columnar antiferromagnet that signals non-negligible magnetic frustration despite the relatively high TN , all the more surprising given its quasi two-dimensional structure. Here, we show, by combining ab initio and model calculations, that the magnetic transition is an order-from-disorder phenomenon, which not only drives the columnar magnetic order, but also the inter-layer coherence responsible for the finite Néel transition temperature. This uncommon ordering mechanism, actively contributed by orbital degrees of freedom, hints at an abundance of low energy excitations above and across the Néel transition, in agreement with experimental evidence.