The detection of gravitational waves from binary neutron stars is a major goal of the gravitational-wave observatories Advanced LIGO and Advanced Virgo . Previous searches for binary neutron stars with LIGO and Virgo neglected the component stars ’ angular momentum ( spin ) . We demonstrate that neglecting spin in matched-filter searches causes advanced detectors to lose more than 3 % of the possible signal-to-noise ratio for 59 % ( 6 % ) of sources , assuming that neutron star dimensionless spins , c \mathbf { J } / GM ^ { 2 } , are uniformly distributed with magnitudes between 0 and 0.4 ( 0.05 ) and that the neutron stars have isotropically distributed spin orientations . We present a new method for constructing template banks for gravitational wave searches for systems with spin . We present a new metric in a parameter space in which the template placement metric is globally flat . This new method can create template banks of signals with non-zero spins that are ( anti- ) aligned with the orbital angular momentum . We show that this search loses more than 3 % of the maximium signal-to-noise for only 9 % ( 0.2 % ) of BNS sources with dimensionless spins between 0 and 0.4 ( 0.05 ) and isotropic spin orientations . Use of this template bank will prevent selection bias in gravitational-wave searches and allow a more accurate exploration of the distribution of spins in binary neutron stars .