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, dz = 123.3 or an absorption path, dX = 229.7. Within this survey path, we identify 4 DLAs, defined as absorbers with HI column density N(HI) >= 10^20.3cm-2, which implies an incidence per absorption length, l(X)= 0.017(+0.014-0.008) at a median survey path redshift of z=0.623. While our estimate of l(X) is lower than earlier estimates at z ~ 0 from HI 21cm emission studies, the results are consistent within the measurement uncertainties. Our dataset 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 = 0.25(+0.20-0.12) x 10^8 Msol Mpc-3. 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 10 Gyrs.
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