We present Keck-I MOSFIRE spectroscopy in the Y and H bands of GDN-8231, a massive, compact, star-forming galaxy (SFG) at a redshift $zsim1.7$. Its spectrum reveals both H$_{alpha}$ and [NII] emission lines and strong Balmer absorption lines. The H$_{alpha}$ and Spitzer MIPS 24 $mu$m fluxes are both weak, thus indicating a low star formation rate of SFR $lesssim5-10$ M$_{odot}$ yr$^{-1}$. This, added to a relatively young age of $sim700$ Myr measured from the absorption lines, provides the first direct evidence for a distant galaxy being caught in the act of rapidly shutting down its star formation. Such quenching allows GDN-8231 to become a compact, quiescent galaxy, similar to 3 other galaxies in our sample, by $zsim1.5$. Moreover, the color profile of GDN-8231 shows a bluer center, consistent with the predictions of recent simulations for an early phase of inside-out quenching. Its line-of-sight velocity dispersion for the gas, $sigma^{rm{gas}}_{!_{rm LOS}}=127pm32$ km s$^{-1}$, is nearly 40% smaller than that of its stars, $sigma^{star}_{!_{rm LOS}}=215pm35$ km s$^{-1}$. High-resolution hydro-simulations of galaxies explain such apparently colder gas kinematics of up to a factor of $sim1.5$ with rotating disks being viewed at different inclinations and/or centrally concentrated star-forming regions. A clear prediction is that their compact, quiescent descendants preserve some remnant rotation from their star-forming progenitors.
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