  Ground-based gravitational wave detectors may be able to constrain the
nuclear equation of state using the early, low frequency portion of the signal
of detected neutron star - neutron star inspirals. In this early adiabatic
regime, the influence of a neutron star's internal structure on the phase of
the waveform depends only on a single parameter lambda of the star related to
its tidal Love number, namely the ratio of the induced quadrupole moment to the
perturbing tidal gravitational field. We analyze the information obtainable
from gravitational wave frequencies smaller than a cutoff frequency of 400 Hz,
where corrections to the internal-structure signal are less than 10 percent.
For an inspiral of two non-spinning 1.4 solar mass neutron stars at a distance
of 50 Mpc, LIGO II detectors will be able to constrain lambda to lambda < 2.0
10^{37} g cm^2 s^2 with 90% confidence. Fully relativistic stellar models show
that the corresponding constraint on radius R for 1.4 solar mass neutron stars
would be R < 13.6 km (15.3 km) for a n=0.5 (n=1.0) polytrope.
