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 HI column density N_HI_>=10^20.3^/cm2, which implies an incidence per absorption length lDLA(X)=0.017_-0.008_^+0.014^ at a median survey path redshift of z=0.623. While our estimate of l_DLA_(X) is lower than earlier estimates at z~0 from HI 21cm emission studies, the results are consistent within the measurement uncertainties. Our data set is too small to properly sample the N_HI_ frequency distribution function f(N_HI_,X), but the observed distribution agrees with previous estimates at z>2. Adopting the z>2 shape of f(N_HI_, X), we infer an HI mass density at z~0.6 of {rho}_HI_^DLA^=0.25_-0.12_^+0.20^. This is significantly lower than previous estimates from targeted DLA surveys with the HST, but consistent with results from low-z HI 21cm observations, and suggests that the neutral gas density of the universe has been decreasing over the past 10Gyr.