We present a search for gravitational waves from double neutron star binaries inspirals in Advanced LIGOs first observing run. The search considers a narrow range of binary chirp masses motivated by the population of known double neutron star binaries in the nearby universe. This search differs from previously published results by providing the most sensitive published survey of neutron stars in Advanced LIGOs first observing run within this narrow mass range and including times when only one of the two LIGO detectors was in operation in the analysis. The search was sensitive to binary neutron star inspirals to an average distance of ~85 Mpc over 93.2 days. We do not identify any unambiguous gravitational wave signals in our sample of 103 sub-threshold candidates with false-alarm-rates of less than one per day. However, given the expected binary neutron star merger rate of R = 100 - 4000 Gpc^(-3) yr^(-1), we expect O(1) gravitational wave events within our candidate list. This suggests the possibility that one or more of these candidates is in fact a binary neutron star merger. Although the contamination fraction in our candidate list is ~99%, it might be possible to correlate these events with other messengers to identify a potential multi-messenger signal. We provide an online candidate list with the times and sky locations for all events in order to enable multi-messenger searches.
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