  We report HI 21-cm line observations of the AGB star X Her obtained with the
Green Bank Telescope (GBT) and the Very Large Array (VLA). We have detected HI
emission totaling M_HI=2.1e-03 M_sun associated with the circumstellar envelope
of the star. The HI distribution exhibits a head-tail morphology, similar to
those previously observed around Mira and RS Cnc. The tail extends ~6.0' (0.24
pc) in the plane of the sky, along the direction of the star's space motion. We
also detect a velocity gradient of ~6.5 km/s across the envelope, consistent
with the HI tracing a turbulent wake that arises from the motion of a
mass-losing star through the ISM. GBT mapping of a 2x2deg region around X Her
reveals that the star lies (in projection) near the periphery of a much larger
HI cloud that also exhibits signatures of ISM interaction. The properties of
the cloud are consistent with those of compact high-velocity clouds. Using CO
observations, we have placed an upper limit on its molecular gas content of
N_H2<1.3e20 cm^-2. Although the distance to the cloud is poorly constrained,
the probability of a chance coincidence in position, velocity, and apparent
position angle of space motion between X Her and the cloud is extremely small,
suggesting a possible physical association. However, the large HI mass of the
cloud (~>2.4~M_sun) and the blueshift of its mean velocity relative to X Her
are inconsistent with an origin tied directly to stellar ejection. (abridged)
