  We present the mid-infrared (5-12 $\mu$m) phase curve of GJ 367b observed by
the Mid-Infrared Instrument (MIRI) on the James Webb Space Telescope (JWST). GJ
367b is a hot (T_eq=1370 K), extremely dense (10.2 +- 1.3 g/cm^3) sub-Earth
orbiting a M dwarf on a 0.32 d orbit. We measure an eclipse depth of 79 +- 4
ppm, a nightside planet-to-star flux ratio of 4 +- 8 ppm, and a relative phase
amplitude of 0.97 +- 0.10 -- all fully consistent with a zero-albedo planet
with no heat recirculation. Su ch a scenario is also consistent with the phase
offset of 11 +- 5 degrees East to within 2.2$\sigma$. The emission spectrum is
likewise consistent with a blackbody with no heat redistribution and a low
albedo of A_B ~ 0.1, with the exception of one anomalous wavelength bin that we
attribute to unexplained systematics. The emission spectrum puts few
constraints on the surface composition, but rules out a CO2 atmosphere >~ 1
bar, an outgassed atmosphere >~10 mbar (under heavily reducing conditions), or
an outgassed atmosphere >~0.01 mbar (under heavily oxidizing conditions). The
lack of day-night heat recirculation implies that 1 bar atmospheres are ruled
out for a wide range of compositions, while 0.1 bar atmospheres are consistent
with the data. Taken together with the fact that most of the dayside should be
molten, our JWST observations suggest the planet must have lost the vast
majority of its initial inventory of volatiles.
