  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.
