  This work presents a new detection of H$_2$ absorption arising in a high
velocity cloud (HVC) associated with either the Milky Way or the Large
Magellanic Cloud (LMC). The absorber was found in an archival Far Ultraviolet
Spectroscopic Explorer spectrum of the LMC star Sk-70$^\circ$32. This is the
fifth well-characterized H$_2$ absorber to be found in the Milky Way's halo and
the second such absorber outside the Magellanic Stream and Bridge. The absorber
has a local standard of rest central velocity of $+$140 km s$^{-1}$ and a H$_2$
column density of $10^{17.5}$ cm$^{-2}$. It is most likely part of a cool and
relatively dense inclusion ($T\approx 75$ K, $n_{\rm H}\sim 100$ cm$^{-3}$) in
a warmer and more diffuse halo cloud. This halo cloud may be part of a
still-rising Milky Way Galactic fountain flow or an outflow from the Large
Magellanic Cloud.
