We investigate the magnetic ground state of CuNdO
2, which is a delafossite with a triangular lattice of magnetic Nd
3+ ions that are well separated by non-magnetic Cu spacer layers. From inelastic neutron scattering measurements of the crystal electric field, we determine the strong Ising character of the pseudo-spin
21 Nd
3+ moments. Magnetic susceptibility and heat capacity measurements reveal the onset of long-range antiferromagnetic order at
TN=0.78 K. While the magnetic transition is definitively observed with muon spin relaxation, accompanied by the formation of a weakly dispersing spin wave excitation, no dipole-ordered moment is detected with neutron diffraction. We show that the apparent absence of a dipolar ordered moment is a consequence of the dominant Ising character of the Nd
3+ moments, which experience extreme frustration on the triangular lattice. Consequently, the frustration in CuNdO
2 is relieved through in-plane ordering of the substantially smaller perpendicular component of the Nd
3+ moments into a 120\textdegree\ structure, with a nearly vanishing ordered moment.