We present the results of the first transient survey from the Owens Valley Radio Observatory Long Wavelength Array (OVRO-LWA) using 31 hr of data, in which we place the most constraining limits on the instantaneous transient surface density at timescales of 13 s to a few minutes and at frequencies below 100 MHz. The OVRO-LWA is a dipole array that images the entire viewable hemisphere with 58 MHz of bandwidth from 27 to 84 MHz at 13 s cadence. No transients are detected above a 6.5$sigma$ flux density limit of 10.5 Jy, implying an upper limit to the transient surface density of $2.5times10^{-8}$ deg$^{-2}$ at the shortest timescales probed, which is orders of magnitude deeper than has been achieved at sub-100 MHz frequencies and comparable flux densities to date. The nondetection of transients in the OVRO-LWA survey, particularly at minutes-long timescales, allows us to place further constraints on the rate of the potential population of transients uncovered by Stewart et al. (2016). From their transient rate, we expect a detection of $8.4^{+31.8}_{-8.0}$ events, and the probability of our null detection is $1.9^{+644}_{-1.9}times10^{-3}$, ruling out a transient rate $>1.4times10^{-4} text{days}^{-1} text{deg}^{-2}$ with 95% confidence at a flux density limit of 18.1 Jy, under the assumption of a flat spectrum and wide bandwidth. We discuss the implications of our nondetection for this population and further constraints that can be made on the source spectral index, intrinsic emission bandwidth, and resulting luminosity distribution.
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