We present the first results from the first Caltech-Jodrell Bank VLBI survey (the CJ1 survey). The CJ1 sample includes 135 radio sources with total flux density 1.3 Jy > S-6 cm greater than or equal to 0.7 Jy, declination delta(1950) greater than or equal to 35 degrees, and Galactic latitude \b(II)\ > 10 degrees. It extends the nux density limit of the complete ''PR'' sample studied by Pearson and Readhead from 1.3 to 0.7 Jy and increases the total number of sources from 65 to 200. The complete survey includes VLBI images at both lambda-18 and 6 cm of all the objects in the extended sample that have cores strong enough to be mapped with the Mark II VLBI system. These images provide a large enough sample to study, for example, the variety of morphologies exhibited by compact radio sources, cosmological evolution, superluminal motion, and misalignment between parsec-scale and kiloparsec-scale radio structures. In this paper we present lambda-18 cm VLBI observations of 56 CJ1 and 31 PR sources made in 1990-1991, including images of 82 sources. The observations were made with a ''snapshot'' technique in which each source was observed in three 20-30-minute scans using an array of 12-16 antennas. The images have resolution 3-10 mas and dynamic range greater than 100:1. Later papers in the series will present the remaining lambda-18 cm observations, the lambda-6 cm observations, and the analysis and interpretation ofthe results.