We report the discovery of two planets, a hot Jupiter (HJ) and a nearby outer sub-Neptune, orbiting the star TOI-4468. This system is unique among the current exoplanet census in that it features a close outer companion to a HJ without an accompanying inner companion. By jointly fitting radial velocity (RV) measurements taken with the NEID spectrograph and transit photometry from the Transiting Exoplanet Survey Satellite (TESS) and several ground-based observatories, we constrain the orbital periods, masses, and radii of these two planets. We confirm the planetary nature of the HJ TOI-4468 b (R = 1.01RJ, m = 0.54MJ, P = 2.77 days). We also validate the outer planet TOI-4468 c (R = 0.28RJ, P = 7.01 days) statistically, incorporating constraints from ground-based observations. We also identify, but cannot confirm, an additional RV signal that may be due to an outer giant in this system with an orbital period of 624 days. From the observed geometry of this system, we argue that it must never have encountered an early secular resonance that is thought to excite the mutual inclination of other HJ/outer companion systems. We discuss the possibility of an undetected inner companion, as well as potential implications for HJ formation.