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We cross-identified the ROSAT Bright Source Catalog (RBSC) and the NRAO VLASky Survey (NVSS) to construct the RBSC-NVSS sample of the brightest X-raysources (>= 0.1 counts/s or ~1E-12 ergs/cm/cm/s in the 0.1-2.4 keV band) thatare also radio sources (S >= 2.5 mJy at 1.4 GHz) in the 7.8 sr of extragalacticsky with |b| > 15 degrees. and delta > -40 degrees. The sky density of NVSSsources is low enough that they can be reliably identified with RBSC sourceshaving average rms positional uncertainties = 10 arcsec. We used the moreaccurate radio positions to make reliable X-ray/radio/optical identificationsdown to the POSS plate limits. We obtained optical spectra for many of thebright identifications lacking published redshifts. The resulting X-ray/radiosample is unique in its size (N ~ 1500 objects), composition (a mixture ofnearly normal galaxies, Seyfert galaxies, quasars, and clusters), and lowaverage redshift (<z> ~ 0.1).Comment: 35 LaTeX pages including 6 eps figures + 40 LaTeX page table2  (landscape) w/ AASTeX 5.0; accepted to ApJ

RBSC‐NVSS Sample. I. Radio and Optical Identifications of a Complete Sample of 1556 Bright X‐Ray Sources