This work presents a new detection of H2 absorption arising in a high-velocity cloud 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°32. This is the fifth well-characterized H2 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 H2 column density of 1017.5 cm−2. It is most likely part of a cool and relatively dense inclusion (T ≈ 75 K, n H ∼ 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.