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 stars 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)
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