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We report the discovery of a low mass-ratio planet $(q = 1.3\times10^{-4})$,i.e., 2.5 times higher than the Neptune/Sun ratio. The planetary system wasdiscovered from the analysis of the KMT-2017-BLG-0165 microlensing event, whichhas an obvious short-term deviation from the underlying light curve produced bythe host of the planet. Although the fit improvement with the microlensparallax effect is relatively low, one component of the parallax vector isstrongly constrained from the light curve, making it possible to narrow downthe uncertainties of the lens physical properties. A Bayesian analysis yieldsthat the planet has a super-Neptune mass $(M_{2}=34_{-12}^{+15}~M_{\oplus})$orbiting a Sun-like star $(M_{1}=0.76_{-0.27}^{+0.34}~M_{\odot})$ located at$4.5~{\rm kpc}$. The blended light is consistent with these host properties.The projected planet-host separation is $a_{\bot}={3.45_{-0.95}^{+0.98}}~{\rmAU}$, implying that the planet is located outside the snowline of the host,i.e., $a_{sl}\sim2.1~{\rm AU}$. KMT-2017-BLG-0165Lb is the sixteenthmicrolensing planet with mass ratio $q<3\times10^{-4}$. Using the fifteen ofthese planets with unambiguous mass-ratio measurements, we apply a likelihoodanalysis to investigate the form of the mass-ratio function in this regime. Ifwe adopt a broken power law for the form of this function, then the break is at$q_{\rm br}\simeq0.55\times10^{-4}$, which is much lower than previouslyestimated. Moreover, the change of the power law slope, $\zeta>3.3$ is quitesevere. Alternatively, the distribution is also suggestive of a "pile-up" ofplanets at Neptune-like mass ratios, below which there is a dramatic drop infrequency.

KMT-2017-BLG-0165Lb: A Super-Neptune mass planet Orbiting a Sun-like Host Star