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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 SDSS Stripe82 region. The CNSS will deliver five epochs over the entire $\sim$270 deg$^2$of Stripe 82, an eventual deep combined map with a rms noise of $\sim$40$\mu$Jy and catalogs at a frequency of 3 GHz, and having a spatial resolutionof 3". This first paper presents the results from an initial pilot survey of a50 deg$^2$ region of Stripe 82, involving four epochs spanning logarithmictimescales between one week and 1.5 years, with the combined map having amedian rms noise of 35 $\mu$Jy. This pilot survey enabled the development ofthe hardware and software for rapid data processing, as well as transientdetection and follow-up, necessary for the full 270 deg$^2$ survey.Classification of variable and transient sources relied heavily on the wealthof multi-wavelength data in the Stripe 82 region, supplemented by repeatedmapping of the region by the Palomar Transient Factory. $3.9^{+0.5}_{-0.9}$% ofthe detected point sources were found to vary by greater than 30%, consistentwith similar studies at 1.4 GHz and 5 GHz. Multi-wavelength photometric dataand light curves suggest that the variability is mostly due to shock-inducedflaring in the jets of AGN. Although this was only a pilot survey, we detectedtwo bona fide transients, associated with an RS CVn binary and a dKe star.Comparison with existing radio survey data revealed additional highly variableand transient sources on timescales between 5-20 years, largely associated withrenewed AGN activity. The rates of such AGN possibly imply episodes of enhancedaccretion and jet activity occurring once every $\sim$40,000 years in thesegalaxies. We compile the revised radio transient rates and make recommendationsfor future transient surveys and joint radio-optical experiments. (Abridged)

The Caltech-NRAO Stripe 82 Survey (CNSS) Paper I: The Pilot Radio Transient Survey In 50 deg$^2$