We present 1-5{mu}m spectroscopy of the coldest known brown dwarf, WISEJ085510.83-071442.5 (WISE0855), performed with the Near-Infrared Spectrograph (NIRSpec) on board the James Webb Space Telescope (JWST). NIRSpec has dramatically improved the measurement of the spectral energy distribution (SED) of WISE0855 in terms of wavelength coverage, signal-to-noise ratios, and spectral resolution. We have performed preliminary modeling of the NIRSpec data using the ATMO 2020 models of cloudless atmospheres, arriving at a best- fitting model that has Teff=285K. That temperature is ~20K higher than the value derived by combining our luminosity estimate with evolutionary models (i.e., the radius in the model fit to the SED is somewhat smaller than expected from evolutionary models). Through comparisons to the model spectra, we detect absorption in the fundamental band of CO, which is consistent with an earlier detection in a ground-based spectrum and indicates the presence of vertical mixing. Although PH3 is expected in Y-dwarfs that experience vertical mixing, it is not detected in WISE0855. Previous ground-based M-band spectroscopy of WISE0855 has been cited for evidence of H2O ice clouds, but we find that the NIRSpec data in that wavelength range are matched well by our cloudless model. Thus, clear evidence of H2O ice clouds in WISE 0855 has not been identified yet, but it may still be present in the NIRSpec data. The physical properties of WISE0855, including the presence of H2O clouds, can be better constrained by more detailed fitting with both cloudless and cloudy models and the incorporation of unpublished 5-28{mu}m data from the Mid-infrared Instrument on JWST.