Observations with the Green Bank Telescope of 21cm HI emission from the high-velocity cloud Complex H suggest that it is interacting with the Milky Way. A model in which the cloud is a satellite of the Galaxy in an inclined, retrograde circular orbit reproduces both the cloud’s average velocity and its velocity gradient with latitude. The model places Complex H at approximately 33 kpc from the Galactic Center on a retrograde orbit inclined about 45 degrees to the Galactic plane. At this location it has an HI mass > 6 10^6 Msun and dimensions of at least 10 by 5 kpc. Some of the diffuse HI associated with the cloud has apparently been decelerated by interaction with Galactic gas. Complex H has similarities to the dwarf irregular galaxy Leo A and to some compact high-velocity clouds, and has an internal structure nearly identical to parts of the Magellanic Stream, with a pressure P/k about 100 cm^{-3} K.

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