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+0.00047−0.00044 days and has a radius of 1.586±0.098 R⊕. The outer planets are sub-Neptunes, with potential gaseous envelopes, having radii of 2.068+0.10−0.091 R⊕, 2.72±0.11 R⊕, and 3.12+0.13−0.12 R⊕ and periods of 6.20370+0.00064−0.00052 days, 14.17555+0.00099−0.0011 days, and 19.5917+0.0022−0.0020 days, respectively. With V and Ks 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⋆=0.888±0.017 R⊙, Teff=5730±50 K), making HD 108236 an exciting, opportune cosmic laboratory for testing models of planet formation and evolution.