  We present JWST and Hubble Space Telescope (HST) observations of the
afterglow of GRB 221009A, the brightest gamma-ray burst (GRB) ever observed.
This includes the first mid-IR spectra of any GRB, obtained with JWST/NIRSPEC
(0.6-5.5 micron) and MIRI (5-12 micron), 12 days after the burst. Assuming that
the intrinsic spectral slope is a single power-law, with $F_{\nu} \propto
\nu^{-\beta}$, we obtain $\beta \approx 0.35$, modified by substantial dust
extinction with $A_V = 4.9$. This suggests extinction above the notional
Galactic value, possibly due to patchy extinction within the Milky Way or dust
in the GRB host galaxy. It further implies that the X-ray and optical/IR
regimes are not on the same segment of the synchrotron spectrum of the
afterglow. If the cooling break lies between the X-ray and optical/IR, then the
temporal decay rates would only match a post jet-break model, with electron
index $p<2$, and with the jet expanding into a uniform ISM medium. The shape of
the JWST spectrum is near-identical in the optical/nIR to X-shooter
spectroscopy obtained at 0.5 days and to later time observations with HST. The
lack of spectral evolution suggests that any accompanying supernova (SN) is
either substantially fainter or bluer than SN 1998bw, the proto-type GRB-SN.
Our HST observations also reveal a disc-like host galaxy, viewed close to
edge-on, that further complicates the isolation of any supernova component. The
host galaxy appears rather typical amongst long-GRB hosts and suggests that the
extreme properties of GRB 221009A are not directly tied to its galaxy-scale
environment.
