We report on a search for radio transients at 340 MHz with the Jansky Very Large Array (VLA) Low band Ionospheric and Transient Experiment (VLITE). Between 2015 July 29 and 2015 September 27, operating in commensal mode, VLITE imaged approximately 2800 pointings covering 12,000 deg$^2$ on the sky, sampling timescales ranging from tens of seconds to several hours on a daily basis. In addition, between 2015 February 25 and 2015 May 9, VLITE observed 55 epochs of roughly 2-4 hours each toward the COSMOS field. Using existing radio source catalogs we have searched all the daily VLITE images for transients, while for the COSMOS field we compared individual images and the summed image to search for new sources in repeated observations of the same field. The wide range of timescales makes VLITE sensitive to both coherent and incoherent transient source classes. No new transients are found, allowing us to set stringent upper limits on transients at milliJansky levels and at low frequencies where comparatively few such surveys have been carried out to date. An all-sky isotropic rate of bursting radio transients with similar rates, duration, and intensity as the unusual transient GCRT J1745$-$3009, discovered in wide-field monitoring toward the Galactic center, is ruled out with high confidence. The resulting non-detections allows us to argue that this is a coherent source, whose properties most resemble the growing class of nulling pulsars. We end with a discussion of the future prospects for the detection of transients by VLITE and other experiments.
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