We present the first spectral search for neutron stars (NSs) in low-mass X-ray binaries (LMXBs) between outbursts in the Small Magellanic Cloud (SMC). We identify and discuss candidate LMXBs in quiescence in the SMC using deep Chandra X-ray observations of two portions of the SMC. We produce X-ray color-magnitude-diagrams of XRSs of these two fields and identify 10 candidates for quiescent NS LMXBs. Spectral fitting and searches for optical counterparts rule out five, leaving five candidate quiescent NS LMXBs. We estimate that we are sensitive to ~10% of quiescent NS LMXBs in our fields. Our fields include 4.410^7 M of stellar mass, giving an upper limit of 10^{6} LMXBs per M in the SMC. We place a lower limit on the average duty cycle of NS LMXBs as ~0.003.

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