This is the first in a series of papers discussing the properties of a complete set of radio sources selected near S_408_ = 1 Jy. We present optical or infrared identifications for a sample of 452 radio galaxies. The sources were selected from the 408 MHz Molonglo Reference Catalog, restricted only by flux density and position on the sky, as follows: S_408_ >= 0.95 Jy and -30^deg^ < decl. (1950) <-20^deg^, and 9^h^20^m^ < R.A.(1950) < 14^h^4^m^ or 20^h^20^m^ < R.A.(1950) < 6^h^14^m^. This complete sample, the MRC/1 Jy survey, contains 558 radio galaxies or quasars, of which six are occulted by bright stars or galaxies and two are multiple confused sources. Of the remaining 550 sources, 527, or 96%, are identified to an r magnitude of 25, and eight additional sources are identified to K = 19. Of the 17 unocculted objects that remain unidentified, 15 are sources for which we have either poor radio maps or inadequate optical/IR images. This paper presents finding charts and astrometric positions for the 452 sources that are not identified as either quasars or BL Lacertae objects. Magnitudes in the r passband accurate to typically 0.1 mag are given for 353 of the radio galaxy identifications. Redshifts for 268 of the galaxies are also listed; these have been derived from 450 spectroscopic observations. The radio observations, quasar and BL Lac identifications, spectroscopy, and near- IR images will be presented in subsequent papers in this series.