We present Neutron Star Interior Composition Explorer (NICER) observations of the neutron star low-mass X-ray binary Serpens X-1 during the early mission phase in 2017. With the high spectral sensitivity and low-energy X-ray passband of NICER, we are able to detect the Fe L line complex in addition to the signature broad, asymmetric Fe K line. We confirm the presence of these lines by comparing the NICER data to archival observations with XMM-Newton/RGS and NuSTAR. Both features originate close to the innermost stable circular orbit (ISCO). When modeling the lines with the relativistic line model RELLINE, we find the Fe L blend requires an inner disk radius of $1.4_{-0.1}^{+0.2}$ $R_{mathrm{ISCO}}$ and Fe K is at $1.03_{-0.03}^{+0.13}$ $R_{mathrm{ISCO}}$ (errors quoted at 90%). This corresponds to a position of $17.3_{-1.2}^{+2.5}$ km and $12.7_{-0.4}^{+1.6}$ km for a canonical neutron star mass ($M_{mathrm{NS}}=1.4 M_{odot}$) and dimensionless spin value of $a=0$. Additionally, we employ a new version of the RELXILL model tailored for neutron stars and determine that these features arise from a dense disk and supersolar Fe abundance.
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