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Protons and neutrons in the atomic nucleus move in shells analogous to the electronic shell structures of atoms. The nuclear shell structure varies as a result of changes in the nuclear mean field with the number of neutrons Nand protons Z, and these variations can be probed by measuring the mass differences between nuclei. The N= Z= 40 self-conjugate nucleus 80Zr is of particular interest, as its proton and neutron shell structures are expected to be very similar, and its ground state is highly deformed. Here we provide evidence for the existence of a deformed double-shell closure in 80Zr through high-precision Penning trap mass measurements of 80–83Zr. Our mass values show that 80Zr is substantially lighter, and thus more strongly bound than predicted. This can be attributed to the deformed shell closure at N= Z= 40 and the large Wigner energy. A statistical Bayesian-model mixing analysis employing several global nuclear mass models demonstrates difficulties with reproducing the observed mass anomaly using current theory.