  We show how to measure cosmological parameters using observations of
inspiraling binary neutron star or black hole systems in one or more
gravitational wave detectors. To illustrate, we focus on the case of fixed mass
binary systems observed in a single Laser Interferometer Gravitational-wave
Observatory (LIGO)-like detector. Using realistic detector noise estimates, we
characterize the rate of detections as a function of a threshold
signal-to-noise ratio $\rho_0$, the Hubble constant $H_0$, and the binary
``chirp'' mass. For $\rho_0 = 8$, $H_0 = 100$ km/s/Mpc, and $1.4 \msun$ neutron
star binaries, the sample has a median redshift of $0.22$. Under the same
assumptions but independent of $H_0$, a conservative rate density of coalescing
binaries ($8\times10^{-8}\,{\rm yr}^{-1}\,{\rm Mpc}^{-3}$) implies LIGO will
observe $\sim 50\,{\rm yr}^{-1}$ binary inspiral events. The precision with
which $H_0$ and the deceleration parameter $q_0$ may be determined depends on
the number of observed inspirals. For fixed mass binary systems, $\sim 100$
observations with $\rho_0 = 10$ in the LIGO detector will give $H_0$ to 10\% in
an Einstein-DeSitter cosmology, and 3000 will give $q_0$ to 20\%. For the
conservative rate density of coalescing binaries, 100 detections with $\rho_0 =
10$ will require about 4~yrs.
