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Since its launch in 2009, the Kepler telescope has found thousands of planets with radii between that of Earth and Neptune. Recent studies of the distribution of these planets have revealed a gap in the population near 1.5-2.0 R ⊕, informally dividing these planets into "super-Earths" and "sub-Neptunes." The origin of this division is difficult to investigate directly because the majority of planets found by Kepler orbit distant, dim stars and are not amenable to radial velocity follow-up or transit spectroscopy, making bulk density and atmospheric measurements difficult. Here, we present the discovery and validation of a newly found planet in direct proximity to the radius gap, orbiting the bright (J = 8.32 mag), nearby (D = 44.5 pc) high proper motion K3.5V star Wolf 503 (EPIC 212779563). We determine the possibility of a companion star and false positive detection to be extremely low using both archival images and high-contrast adaptive optics images from the Palomar observatory. The brightness of the host star makes Wolf 503b a prime target for prompt radial velocity follow-up, and with the small stellar radius (0.690 ± 0.025R o), it is also an excellent target for HST transit spectroscopy and detailed atmospheric characterization with JWST. With its measured radius near the gap in the planet radius and occurrence rate distribution, Wolf 503b offers a key opportunity to better understand the origin of this radius gap as well as the nature of the intriguing populations of "super-Earths" and "sub-Neptunes" as a whole.