(abridged) We present the HIPASS Bright Galaxy Catalog (BGC) which contains the 1000 HI-brightest galaxies in the southern sky as obtained from the HI Parkes All-Sky Survey (HIPASS). The selection of the brightest sources is based on their HI peak flux density (Speak > 116 mJy) as measured from the spatially integrated HIPASS spectrum. The derived HI masses range from about 10^7 to 4 x 10^10 Msun. While the BGC (z < 0.03) is complete in Speak, only a subset of about 500 sources can be considered complete in integrated HI flux density (FHI > 25 JY km/s). The HIPASS BGC contains a total of 158 new redshifts and yields no evidence for a population of free-floating intergalactic HI clouds without associated optical counterparts. HIPASS provides a clear view of the local large-scale structure. The dominant features in the sky distribution of the BGC are the Supergalactic Plane and the Local Void. In addition, one can clearly see the Centaurus Wall which connects via the Hydra and Antlia clusters to the Puppis filament. Some previously hardly noticed galaxy groups stand out quite distinctively in the HI sky distribution. Several new structures are seen for the first time, not only behind the Milky Way.