  We present the first exoplanet phase curve measurement made with the JWST
NIRSpec instrument, highlighting the exceptional stability of this
newly-commissioned observatory for exoplanet climate studies. The target,
WASP-121b, is an ultrahot Jupiter with an orbital period of 30.6 hr. We analyze
two broadband light curves generated for the NRS1 and NRS2 detectors, covering
wavelength ranges of 2.70-3.72 micron and 3.82-5.15 micron, respectively. Both
light curves exhibit minimal systematics, with approximately linear drifts in
the baseline flux level of 30 ppm/hr (NRS1) and 10 ppm/hr (NRS2). Assuming a
simple brightness map for the planet described by a low-order spherical
harmonic dipole, our light curve fits suggest that the phase curve peaks
coincide with orbital phases $3.36 \pm 0.11$ deg (NRS1) and $2.66 \pm 0.12$ deg
(NRS2) prior to mid-eclipse. This is consistent with the strongest dayside
emission emanating from eastward of the substellar point. We measure
planet-to-star emission ratios of $3,924 \pm 7$ ppm (NRS1) and $4,924 \pm 9$
ppm (NRS2) for the dayside hemisphere, and $136 \pm 8$ ppm (NRS1) and $630 \pm
10$ ppm (NRS2) for the nightside hemisphere. The latter nightside emission
ratios translate to planetary brightness temperatures of $926 \pm 12$ K (NRS1)
and $1,122 \pm 10$ K (NRS2), which are low enough for a wide range of
refractory condensates to form, including enstatite and forsterite. A nightside
cloud deck may be blocking emission from deeper, hotter layers of the
atmosphere, potentially helping to explain why cloud-free 3D general
circulation model simulations systematically over-predict the nightside
emission for WASP-121b.
