We present the first stellar velocity dispersion measurement of a massive quenching galaxy at z = 4. The galaxy is first identified as a massive z ≥ 4 galaxy with suppressed star formation from photometric redshifts based on deep multiband data. A follow-up spectroscopic observation with MOSFIRE on Keck revealed strong multiple absorption features, which are identified as Balmer lines, giving a secure redshift of z = 4.01. This is the most distant quiescent galaxy known to date. Thanks to the high S/N of the spectrum, we are able to estimate the stellar velocity dispersion, σ =268+/- 59 {km} {{{s}}}^-1, making a significant leap from the previous highest redshift measurement at z = 2.8. Interestingly, we find that the velocity dispersion is consistent with that of massive galaxies today, implying no significant evolution in velocity dispersion over the last 12 Gyr. Based on a stringent upper limit on its physical size from deep optical images (r _eff < 1.3 kpc), we find that its dynamical mass is consistent with the stellar mass inferred from photometry. Furthermore, the galaxy is located on the mass fundamental plane extrapolated from lower redshift galaxies. The observed no strong evolution in σ suggests that the mass in the core of massive galaxies does not evolve significantly, while most of the mass growth occurs in the outskirts of the galaxies, which also increases the size. This picture is consistent with a two-phase formation scenario in which mass and size growth is due to accretion in the outskirts of galaxies via mergers. Our results imply that the first phase may be completed as early as z ∼ 4.