The interpretation of the emergent collective behavior of atomic nuclei in terms of deformed intrinsic shapes is at the heart of our understanding of the rich phenomenology of their structure, ranging from nuclear energy to astrophysical applications across a vast spectrum of energy scales. A new window into the deformation of nuclei has been recently opened with the realization that nuclear collision experiments performed at high-energy colliders, such as the CERN Large Hadron Collider (LHC), enable experimenters to identify the relative orientation of the colliding ions in a way that magnifies the manifestations of their intrinsic deformation. Here we apply this technique to LHC data on collisions of ^{129}Xe nuclei to exhibit the first evidence of nonaxiality in the ground state of ions collided at high energy. We predict that the low-energy structure of ^{129}Xe is triaxial (a spheroid with three unequal axes) and show that such deformation can be determined from high-energy data. This result demonstrates the unique capabilities of precision collider machines such as the LHC as new means to perform imaging of the collective structure of atomic nuclei.