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Hot Jupiters are generally observed to lack close planetary companions, a trend that has been interpreted as evidence for high-eccentricity migration. We present the discovery and validation of WASP-132 c (TOI-822.02), a 1.85 $\pm$ 0.10 $R_{\oplus}$ planet on a 1.01 day orbit interior to the hot Jupiter WASP-132 b. Transiting Exoplanet Survey Satellite (TESS) and ground-based follow-up observations, in conjunction with vetting and validation analysis, enable us to rule out common astrophysical false positives and validate the observed transit signal produced by WASP-132 c as a planet. Running the validation tools \texttt{vespa} and \texttt{triceratops} on this signal yield false positive probabilities of $9.02 \times 10^{-5}$ and 0.0107, respectively. Analysis of archival CORALIE radial velocity data leads to a 3$σ$ upper limit of 28.23 ms$^{-1}$ on the amplitude of any 1.01-day signal, corresponding to a 3$σ$ upper mass limit of 37.35 $M_{\oplus}$. Dynamical simulations reveal that the system is stable within the 3$σ$ uncertainties on planetary and orbital parameters for timescales of $\sim$100 Myr. The existence of a planetary companion near the hot Jupiter WASP-132 b makes the giant planet's formation and evolution via high-eccentricity migration highly unlikely. Being one of just a handful of nearby planetary companions to hot Jupiters, WASP-132 c carries with it significant implications for the formation of the system and hot Jupiters as a population.