One of the main objectives of the Transiting Exoplanet Survey Satellite (TESS) mission is the discovery of small rocky planets around relatively bright nearby stars. Here, we report the discovery and characterization of the transiting super-Earth planet orbiting LHS 1478 (TOI-1640). The star is an inactive red dwarf (J ~ 9.6 mag and spectral type m3 V) with mass and radius estimates of 0.20 ± 0.01M⊙ and 0.25 ± 0.01R⊙, respectively, and an effective temperature of 3381 ± 54 K. It was observed by TESS in four sectors. These data revealed a transit-like feature with a period of 1.949 days. We combined the TESS data with three ground-based transit measurements, 57 radial velocity (RV) measurements from CARMENES, and 13 RV measurements from IRD, determining that the signal is produced by a planet with a mass of 2.33‒0.20+0.20 M⊕ and a radius of 1.24‒0.05+0.05 R⊕. The resulting bulk density of this planet is 6.67 g cm‒3, which is consistent with a rocky planet with an Fe- and MgSiO3-dominated composition. Although the planet would be too hot to sustain liquid water on its surface (its equilibrium temperature is about ~595 K, suggesting aVenus-like atmosphere), spectroscopic metrics based on the capabilities of the forthcoming James Webb Space Telescope and the fact that the host star is rather inactive indicate that this is one of the most favorable known rocky exoplanets for atmospheric characterization.