  We present Hubble Space Telescope observations of the active asteroid (and
Geminid stream parent) 3200 Phaethon when at its closest approach to Earth
(separation 0.07 AU) in 2017 December. Images were recorded within
$\sim$1\degr~of the orbital plane, providing extra sensitivity to low surface
brightness caused by scattering from a large-particle trail. We placed an upper
limit to the apparent surface brightness of such a trail at 27.2 magnitudes
arcsecond$^{-2}$, corresponding to an in-plane optical depth $\le
3\times10^{-9}$. No co-moving sources brighter than absolute magnitude 26.3,
corresponding to circular equivalent radius $\sim$12 m (albedo 0.12 assumed),
were detected. Phaethon is too hot for near-surface ice to survive. We briefly
consider the thermodynamic stability of deeply-buried ice, finding that its
survival would require either a very small (regolith-like) thermal diffusivity
($< 10^{-8}$ m$^2$ s$^{-1}$), or the unexpectedly recent injection of Phaethon
(timescale $\lesssim$ 10$^6$ yr) into its present orbit, or both.
