  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 ($J \sim 9.6$\,mag and spectral type m3\,V) with mass and
radius estimates of $0.20\pm0.01$\,$M_{\odot}$ and $0.25\pm0.01$\,$R_{\odot}$,
respectively, and an effective temperature of $3381\pm54$\,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 $2.33^{+0.20}_{-0.20}$\,$M_{\oplus}$ and a radius of
$1.24^{+0.05}_{-0.05}$\,$R_{\oplus}$. The resulting bulk density of this planet
is 6.67\,g\,cm$^{-3}$, which is consistent with a rocky planet with an Fe- and
MgSiO$_3$-dominated composition. Although the planet would be too hot to
sustain liquid water on its surface (its equilibrium temperature is about
$\sim$595\,K, suggesting a Venus-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.
