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The FIRST survey to produce Faint Images of the Radio Sky at Twenty centimeters is now underway using the NRAO Very Large Array. We describe here the scientific motivation for a large-area sky survey at radio frequencies which has a sensitivity and angular resolution comparable to the Palomar Observatory Sky Survey, and we recount the history that led to the current survey project. The technical design of the survey is covered in detail, including a description and justification of the grid pattern chosen, the rationale behind the integration time and angular resolution selected, and a summary of the other considerations which informed our planning for the project. A comprehensive description of the automated data analysis pipeline we have developed is presented. <P />We also report here the results of the first year of FIRST observations. A total of 144 hr of time in 1993 April and May was used for a variety of tests, as well as to cover an initial strip of the survey extending between 07<SUP>h</SUP> 15<SUP>m</SUP> and 16<SUP>h</SUP> 30<SUP>m</SUP> in a 2°.8 wide declination zone passing through the local zenith (28.2 <δ < 31.0). A total of 2153 individual pointings yielded an image database containing 1039 merged images 46'.5 × 34'.5 in extent with 1".8 pixels and a typical rms of 0.13 mJy. A catalog derived from this 300 deg<SUP>2</SUP> region contains 28,000 radio sources. We have performed extensive tests on the images and source list in order to establish the photometric and astrometric accuracy of these data products. We find systematic astrometric errors of < 0".05 individual sources down to the 1 mJy survey flux density threshold have 90% confidence error circles with radii of < 1". CLEAN bias introduces a systematic underestimate of point-source flux densities of ∼0.25 mJy; the bias is more severe for extended sources. Nonetheless, a comparison with a published deep survey field demonstrates that we successfully detect 39/49 sources with integrated flux densities greater than 0.75 mJy, including 19 of 20 sources above 2.0 mJy; the sources not detected are known to be very extended and so have surface brightnesses well below our threshold. <P />With 480 hr of observing time committed for each of the next three B-configuration periods, FIRST will complete nearly one-half of its goal of covering the 10,000 deg<SUP>2</SUP> of the north Galactic cap scheduled for inclusion in the Sloan Digital Sky Survey. All of the FIRST data raw visibilities, self-calibrated UV data sets, individual pointing maps, final merged images, source catalogs, and individual source images are being placed in the public domain as soon as they are verified; all of the 1993 data are now available through the NRAO and/or the STScI archive. We conclude with a brief summary of the scientific significance of FIRST, which represents an improvement by a factor of 50 in both angular resolution and sensitivity over the best available large area radio surveys.