Using optimal matched filtering, we search 25 hours of data from the LIGO 4
0-m prototype laser interferometric gravitational-wave detector for gravita
tional-wave chirps emitted by coalescing binary systems within our Galaxy.
This is the first test of this filtering technique on real interferometric
data. An upper limit on the rate R of neutron star binary inspirals in our
Galaxy is obtained: with 90% confidence, R < 0.5 h(-1). Similar experiments
with LIGO interferometers will provide constraints on the population of ti
ght binary neutron star systems in the Universe.