  We estimate the coalescence rate of close binaries with two neutron stars
(NS) and discuss the prospects for the detection of NS-NS inspiral events by
ground-based gravitational-wave observatories, such as LIGO. We derive the
Galactic coalescence rate using the observed sample of close NS-NS binaries
(PSR B1913+16 and PSR B1534+12) and examine in detail each of the sources of
uncertainty associated with the estimate. Specifically, we investigate (i) the
dynamical evolution of NS-NS binaries in the Galactic potential and the
vertical scale height of the population, (ii) the pulsar lifetimes, (iii) the
effects of the faint end of the radio pulsar luminosity function and their
dependence on the small number of observed objects, (iv) the beaming fraction,
and (v) the extrapolation of the Galactic rate to extragalactic distances
expected to be reachable by LIGO. We find that the dominant source of
uncertainty is the correction factor (up to about 200) for faint (undetectable)
pulsars. All other sources are much less important, each with uncertainty
factors smaller than 2. Despite the relatively large uncertainty, the derived
coalescence rate is approximately consistent with previously derived upper
limits, and is more accurate than rates obtained from population studies. We
obtain a most conservative lower limit for the LIGO II detection rate of 2
events per year. Our upper limit on the detection rate lies between 300 to more
than 1000 events per year.
