We present the results of a neutral hydrogen survey of 79 galaxies from a statistical sample of 88 Blue Compact Galaxies (BCGs) selected from the First and Second Byurakan objective prism surveys to have a HII region-like spectrum, an equivalent width of the [O III] {lambda}5007 line larger than ~50{AA}, and a velocity <=6000km/s. The detection rate for the statistical sample is 74%. HI masses range between 4x10^7^M_{sun}_ and 5x10^9^M_{sun}_ with the HI mass distribution peaking at 3x10^8^M_{sun}_. The full width at half-maximum of the HI profile varies between ~30km/s and 160km/s, with a mean of ~92km/s. These small widths are characteristic of dwarf galaxies. For comparison, we have also observed an additional 92 BCGs with weaker star formation and/or larger distances, and/or interesting astrophysical properties. These in general have larger widths and HI masses.