For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to its closest predecessor by a directed edge. We show that for every set of n points in \(\mathbb {R}^{d}\) , there exists an order such that the corresponding ordered Nearest Neighbor Graph has maximum degree at least \(\log {n}/(4d)\) . Apart from the 1/(4d) factor, this bound is the best possible. As for the abstract setting, we show that for every n-element metric space, there exists an order such that the corresponding ordered Nearest Neighbor Graph has maximum degree \(\varOmega (\sqrt{\log {n}/\log \log {n}})\) .