We use the Hubble Space Telescope ( HST ) archive of ultraviolet ( UV ) quasar spectroscopy to conduct the first blind survey for damped Ly- \alpha absorbers ( DLAs ) at low redshift ( z < 1.6 ) . Our statistical sample includes 463 quasars with spectral coverage spanning a total redshift path \Delta z = 123.3 or an absorption path \Delta X = 229.7 . Within this survey path , we identify 4 DLAs defined as absorbers with H i column density N _ { H \textsc { i } } \geq 10 ^ { 20.3 } cm ^ { -2 } , which implies an incidence per absorption length \ell _ { DLA } ( X ) = 0.017 ^ { +0.014 } _ { -0.008 } at a median survey path redshift of z = 0.623 . While our estimate of \ell _ { DLA } ( X ) is lower than earlier estimates at z \approx 0 from H i 21 cm emission studies , the results are consistent within the measurement uncertainties . Our dataset is too small to properly sample the N _ { H \textsc { i } } frequency distribution function f ( N _ { H \textsc { i } } ,X ) , but the observed distribution agrees with previous estimates at z > 2 . Adopting the z > 2 shape of f ( N _ { H \textsc { i } } ,X ) , we infer an H i mass density at z \sim 0.6 of \rho _ { H \textsc { i } } ^ { DLA } = 0.25 ^ { +0.20 } _ { -0.12 } \times 10 ^ { 8 } M _ { \odot } Mpc ^ { -3 } . This is significantly lower than previous estimates from targeted DLA surveys with the HST , but consistent with results from low- z H i 21 cm observations , and suggests that the neutral gas density of the universe has been decreasing over the past 10 Gyrs .