In the underdoped n-type cuprate Nd_2-xCe_xCuO₄, long-range antiferromagnetic order reconstructs the Fermi surface, resulting in a putative antiferromagnetic metal with small Fermi pockets. Using angle-resolved photoemission spectroscopy, we observe an anomalous energy gap, an order of magnitude smaller than the antiferromagnetic gap, in a wide portion of the underdoped regime and smoothly connecting to the superconducting gap at optimal doping. After considering all the known ordering tendencies in tandem with the phase diagram, we hypothesize that the normal-state gap in the underdoped n-type cuprates originates from Cooper pairing. The high temperature scale of the normal-state gap raises the prospect of engineering higher transition temperatures in the n-type cuprates comparable to those of the p-type cuprates.