Broad Fe K emission lines have been widely observed in the X-ray spectra of black hole systems as well as in neutron star systems. The intrinsically narrow Fe K fluorescent line is generally believed to be part of the reflection spectrum originating in an illuminated accretion disk which is broadened by strong relativistic effects. However, the nature of the lines in neutron star low-mass X-ray binaries (LMXBs) has been a matter of debate. We therefore obtained the longest, high-resolution X-ray spectrum of a neutron star LMXB to date with a 300 ks Chandra High Energy Transmission Grating Spectrometer (HETGS) observation of Serpens X-1. The observation was taken under the "continuous clocking" mode, and thus was free of photon pile-up effects. We carry out a systematic analysis and find that the blurred reflection model fits the Fe line of Serpens X-1 significantly better than a broad Gaussian component does, implying that the relativistic reflection scenario is much preferred. Chandra HETGS also provides a highest spectral resolution view of the Fe K region and we find no strong evidence for additional narrow lines.