We report the discovery and validation of four extrasolar planets hosted by the nearby, bright, Sun-like (G3V) star HD 108236 using data from the Transiting Exoplanet Survey Satellite (TESS). We present transit photometry, reconnaissance, and precise Doppler spectroscopy, as well as high-resolution imaging, to validate the planetary nature of the objects transiting HD 108236, also known as the TESS Object of Interest (TOI) 1233. The innermost planet is a possibly rocky super-Earth with a period of 3.79523-(.00047)(0.000440+) days and has a radius of 1.586 +/- 0.098 R-circle plus. The outer planets are sub-Neptunes, with potential gaseous envelopes, having radii of 2.068(-0.091)(+0.10) R-circle plus, 2.72 +/- 0.11 R-circle plus, and 3.12(-0.12)(+0.13) R-circle plus and periods of 6.20370(-0.00052)(+0.00064) days, 14.17555(-0.0011)(+0.00099) days, and 19.5917(-0.0020)(+0.0022) days, respectively. With V and K-s magnitudes of 9.2 and 7.6, respectively, the bright host star makes the transiting planets favorable targets for mass measurements and, potentially, for atmospheric characterization via transmission spectroscopy. HD 108236 is the brightest Sun-like star in the visual (V) band known to host four or more transiting exoplanets. The discovered planets span a broad range of planetary radii and equilibrium temperatures and share a common history of insolation from a Sun-like star (R-a = 0.888 +/- 0.017 R-circle dot, Teff = 5730 +/- 50 K), making HD 108236 an exciting, opportune cosmic laboratory for testing models of planet formation and evolution.