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We report the first discovery of a fast radio burst (FRB), FRB 20200125A, by the Green Bank Northern Celestial Cap (GBNCC) Pulsar Survey conducted with the Green Bank Telescope at 350 MHz. FRB 20200125A was detected at a Galactic latitude of 58.43 degrees with a dispersion measure of 179 pc cm$^{-3}$, while electron density models predict a maximum Galactic contribution of 25 pc cm$^{-3}$ along this line of sight. Moreover, no apparent Galactic foreground sources of ionized gas that could account for the excess DM are visible in multi-wavelength surveys of this region. This argues that the source is extragalactic. The maximum redshift for the host galaxy is $z_{max}=0.17$, corresponding to a maximum comoving distance of approximately 750 Mpc. The measured peak flux density for FRB 20200125A is 0.37 Jy, and we measure a pulse width of 3.7 ms, consistent with the distribution of FRB widths observed at higher frequencies. Based on this detection and assuming an Euclidean flux density distribution of FRBs, we calculate an all-sky rate at 350 MHz of $3.4^{+15.4}_{-3.3} \times 10^3$ FRBs sky$^{-1}$ day$^{-1}$ above a peak flux density of 0.42 Jy for an unscattered pulse having an intrinsic width of 5 ms, consistent with rates reported at higher frequencies. Given the recent improvements in our single-pulse search pipeline, we also revisit the GBNCC survey sensitivity to various burst properties. Finally, we find no evidence of interstellar scattering in FRB 20200125A, adding to the growing evidence that some FRBs have circumburst environments where free-free absorption and scattering are not significant.