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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 $3.79523_{-0.00044}^{+0.00047}$ days and has a radius of $1.586\pm0.098$ $R_\oplus$. The outer planets are sub-Neptunes, with potential gaseous envelopes, having radii of $2.068_{-0.091}^{+0.10}$ $R_\oplus$, $2.72\pm0.11$ $R_\oplus$, and $3.12_{-0.12}^{+0.13}$ $R_\oplus$ 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$_{\rm s}$ 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 ($R_\star = 0.888 \pm 0.017$ R$_\odot$, $T_{\rm eff} = 5730 \pm 50$ K), making HD 108236 an exciting, opportune cosmic laboratory for testing models of planet formation and evolution.