In the presence of strong interactions, the fluid of mobile electrons in a metal can spontaneously break the point group symmetries of its underlying host lattice, forming a quantum analogue of a classical liquid crystal. The experimental discovery of 2D quantum liquid crystals (QLCs) was first made nearly 20 years ago in semiconductor heterostructures and has since been reported in many other systems including the copper- and iron-based high-temperature superconductors. However whether or not a 3D version of a QLC can exist has remained unclear. In this talk, I will present signatures of a 3D QLC in the strongly spin-orbit coupled metallic pyrochore Cd2Re2O7 detected using ultrafast coherent phonon spectroscopy and a recently developed spatially-resolved nonlinear optical polarimetry technique. I will highlight the unusual properties of this 3D QLC that distinguish it from the 2D version and discuss its possible connection to unconventional superconductivity.