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 1.3Jy>S_6cm>=0.7Jy, declination delta_1950>=35deg, and Galactic latitude |b^II|>10deg. It extends the flux density limit of the complete "PR" sample studied by Pearson & Readhead from 1.3 to 0.7Jy and increases the total number of sources from 65 to 200. The complete survey includes VLBI images at both lambda-18 and 6cm of all 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-18cm 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 3-10mas and dynamic range greater than 100:1. Later papers in the series will present the remaining lambda-18cm observations, the lambda-6cm observations, and the analysis and interpretation of the results.