We present the first direct spectroscopic measurement of the stellar velocity dispersion function (VDF) for massive quiescent and star-forming galaxies at 0.6 < z ≤ 1.0. For this analysis we use individual measurements of stellar velocity dispersion from high-signal-to-noise-ratio spectra from the public Large Early Galaxy Astrophysics Census (LEGA-C) survey. We report a remarkable stability of the VDF for both quiescent and star-forming galaxies within this redshift range, though we note the presence of weak evolution in the number densities of star-forming galaxies. We compare both VDFs with previous direct and inferred measurements at local and intermediate redshifts, with the caveat that previous measurements of the VDF for star-forming galaxies are poorly constrained at all epochs. We emphasize that this work is the first to directly push to low stellar velocity dispersion (σ ⋆ > 100 km s−1) and extend to star-forming galaxies. We are largely consistent with the high-sigma tail measured from BOSS, and we find that the VDF remains constant from the median redshift of LEGA-C, z ∼ 0.8, to the present day.