We have commenced a multi-year program, the Caltech-NRAO Stripe 82 Survey (CNSS), to search for radio transients with the Jansky VLA in the Sloan Digital Sky Survey Stripe 82 region. The CNSS will deliver five epochs over the entire ∼270 deg 2 of Stripe 82, an eventual deep combined map with a rms noise of ∼40 µJy and catalogs at a frequency of 3 GHz, and having a spatial resolution of 3. This first paper presents the results from an initial pilot survey of a 50 deg 2 region of Stripe 82, involving four epochs spanning logarithmic timescales between one week and 1.5 years, with the combined map having a median rms noise of 35 µJy. This pilot survey enabled the development of the hardware and software for rapid data processing, as well as transient detection and follow-up, necessary for the full 270 deg 2 survey. Data editing, calibration, imaging, source extraction, cataloging and transient identification were completed in a semi-automated fashion within six hours of completion of each epoch of observations, using dedicated computational hardware at the NRAO in Socorro, and custom-developed data reduction and transient detection pipelines. Classification of variable and transient sources relied heavily on the wealth of multi-wavelength legacy survey data in the Stripe 82 region, supplemented by repeated mapping of the region by the Palomar Transient Factory (PTF). 3.9 +0.5 −0.9 % of the few thousand detected point sources were found to vary by greater than 30%, consistent with similar studies at 1.4 GHz and 5 GHz. Multi-wavelength photometric data and light curves suggest that the variability is mostly due to shock-induced flaring in the jets of AGN. Although this was only a pilot survey, we detected two bona fide transients, associated with an RS CVn binary and a dKe star. Comparison with existing legacy survey data (FIRST, VLA-Stripe 82) revealed additional highly variable and transient sources on timescales between 5-20 years, largely associated with renewed AGN activity. The rates of such AGN possibly imply episodes of enhanced accretion and jet activity occurring once every ∼40,000 years in these galaxies. We compile the revised radio transient rates and make recommendations for future transient surveys and joint radio-optical experiments.