  We report on JWST commissioning observations of the transiting exoplanet
HAT-P-14 b, obtained using the Bright Object Time Series (BOTS) mode of the
NIRSpec instrument with the G395H/F290LP grating/filter combination
($3-5\mu$m). While the data were used primarily to verify that the NIRSpec BOTS
mode is working as expected, and to enable it for general scientific use, they
yield a precise transmission spectrum which we find is featureless down to the
precision level of the instrument, consistent with expectations given
HAT-P-14~b's small scale-height and hence expected atmospheric features. The
exquisite quality and stability of the \emph{JWST/NIRSpec} transit spectrum --
almost devoid of any systematic effects -- allowed us to obtain median
uncertainties of 50-60 ppm in this wavelength range at a resolution of $R=100$
in a single exposure, which is in excellent agreement with pre-flight
expectations and close to the (or at the) photon-noise limit for a $J = 9.094$,
F-type star like HAT-P-14. These observations showcase the ability of
NIRSpec/BOTS to perform cutting-edge transiting exoplanet atmospheric science,
setting the stage for observations and discoveries to be made in Cycle 1 and
beyond.
