  We present thermal infrared observations of the active asteroid (and Geminid
meteoroid stream parent) 3200 Phaethon using the Very Large Telescope. The
images, at 10.7 micron wavelength, were taken with Phaethon at its closest
approach to Earth (separation 0.07 AU) in 2017 December, at a linear resolution
of about 14 km. We probe the Hill sphere (of radius 66 km) for trapped dust and
macroscopic bodies, finding neither, and we set limits to the presence of
unbound dust. The derived limits to the optical depth of dust near Phaethon
depend somewhat on the assumed geometry, but are of order 1e-5. The upper limit
to the rate of loss of mass in dust is 14 kg/s. This is about 50 times smaller
than the rate needed to sustain the Geminid meteoroid stream in steady state.
The observations thus show that the production of the Geminids does not proceed
in steady state.
