We study the aging of a glassy Lennard-Jones binary mixture with molecular dynamics simulations. We follow the evolution of the packing as a function of the system's age tw, the time passed since the system is quenched to below its glass transition temperature. We focus on simple properties of all tetrahedra formed by the majority of particles. We find that both the averages and the distributions of the edge length of tetrahedra and of their standard deviation monotonically evolve over time: they age. Specifically the aging process decreases the irregularity of tetrahedra while loosening them up. This is in stark contrast with previous experiments on slightly charged hard-sphere colloidal suspension where tetrahedral geometry was found to be a poor indicator of age. Furthermore, we confirm that tetrahedral packings sample microscopic structure in a non-trivial way.