SuperSpec is a novel on-chip spectrometer we are developing for multi-object, moderate resolution (R = 100 - 500), large bandwidth (~1.65:1) submillimeter and millimeter survey spectroscopy of high-redshift galaxies. The spectrometer employs a filter bank architecture, and consists of a series of half-wave resonators formed by lithographically-patterned superconducting transmission lines. The signal power admitted by each resonator is detected by a lumped element titanium nitride (TiN) kinetic inductance detector (KID) operating at 100 - 200 MHz. We have tested a new prototype device that achieves the targeted R = 100 resolving power, and has better detector sensitivity and optical efficiency than previous devices. We employ a new method for measuring photon noise using both coherent and thermal sources of radiation to cleanly separate the contributions of shot and wave noise. We report an upper limit to the detector NEP of $1.4times10^{-17}$ W Hz$^{-1/2}$, within 10% of the photon noise limited NEP for a ground-based R=100 spectrometer.