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We report on James Webb Space Telescope (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 μ 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 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. [ABSTRACT FROM AUTHOR]