  Many X-ray binaries remain undetected in the mid-infrared, a regime where
emission from their compact jets is likely to dominate. Here, we report the
detection of the black hole binary GX 339-4 with the Wide-field Infrared Survey
Explorer (WISE) during a very bright, hard accretion state in 2010. Combined
with a rich contemporaneous multiwavelength dataset, clear spectral curvature
is found in the infrared, associated with the peak flux density expected from
the compact jet. An optically-thin slope of ~-0.7 and a jet radiative power of
>6x10^{35} erg/s (d/8 kpc)^2 are measured. A ~24 h WISE light curve shows
dramatic variations in mid-infrared spectral slope on timescales at least as
short as the satellite orbital period ~95 mins. There is also significant
change during one pair of observations spaced by only 11 s. These variations
imply that the spectral break associated with the transition from self-absorbed
to optically-thin jet synchrotron radiation must be varying across the full
wavelength range of ~3-22 microns that WISE is sensitive to, and more. Based on
four-band simultaneous mid-infrared detections, the break lies at ~5x10^{13} Hz
in at least two epochs of observation, consistent with a magnetic field
B~1.5x10^4 G assuming a single-zone synchrotron emission region. The observed
variability implies that either B, or the size of the acceleration zone above
the jet base, are being modulated by factors of ~10 on relatively-short
timescales.
