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 \mbox { $M _ { \odot } $ } 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 \times 10 ^ { -8 } { yr } ^ { -1 } { Mpc } ^ { -3 } ) implies LIGO will observe \sim 50 { 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 .