Strong interactions among electrons in some materials can cause them to assume configurations that are less symmetric than the underlying crystal lattice. These so-called electronic nematic states usually have inversion symmetry, but theorists have predicted that in metals with strong spin-orbit coupling, the inversion symmetry can be lost. Harter et al. teased out the symmetry of the electronic order in the compound Cd2Re2O7 (see the Perspective by Dodge). They found that a known structural transition in this material is a consequence of another, previously hidden electronic order that breaks inversion symmetry. Science, this issue p. 295; see also p. 246 Strong electron interactions can drive metallic systems toward a variety of well-known symmetry-broken phases, but the instabilities of correlated metals with strong spin-orbit coupling have only recently begun to be explored. We uncovered a multipolar nematic phase of matter in the metallic pyrochlore Cd2Re2O7 using spatially resolved second-harmonic optical anisotropy measurements. Like previously discovered electronic nematic phases, this multipolar phase spontaneously breaks rotational symmetry while preserving translational invariance. However, it has the distinguishing property of being odd under spatial inversion, which is allowed only in the presence of spin-orbit coupling. By examining the critical behavior of the multipolar nematic order parameter, we show that it drives the thermal phase transition near 200 kelvin in Cd2Re2O7 and induces a parity-breaking lattice distortion as a secondary order.