We report H i 21-cm line observations of the asymptotic giant branch ( AGB ) star X Her obtained with the Robert C. Byrd Green Bank Telescope ( GBT ) and the Very Large Array ( VLA ) . We have unambiguously detected H i emission associated with the circumstellar envelope of the star , with a mass totaling M _ { HI } \approx 2.1 \times 10 ^ { -3 } ~ { } M _ { \odot } . The H i distribution exhibits a head-tail morphology , similar to those previously observed around the AGB stars Mira and RS Cnc . The tail is elongated along the direction of the star ’ s space motion , with a total extent of ~ { } \hbox to 0.0 pt { $ > $ } { \lower 4.3 pt \hbox { $ \sim$ } } 6 ^ { \prime } \hskip { -4.836969 pt } . \hskip { 0.0 pt } 0 ( 0.24 pc ) in the plane of the sky . We also detect a systematic radial velocity gradient of \sim 6.5 km s ^ { -1 } across the H i envelope . These results are consistent with the H i emission tracing a turbulent wake that arises from the motion of a mass-losing star through the interstellar medium ( ISM ) . GBT mapping of a 2 ^ { \circ } \times 2 ^ { \circ } region around X Her reveals that the star lies ( in projection ) near the periphery of a much larger H i cloud that also exhibits signatures of interaction with the ISM . The properties of the cloud are consistent with those of compact high-velocity clouds . Using ^ { 12 } CO J =1-0 observations , we have placed an upper limit on its molecular gas content of N _ { H 2 } < 1.3 \times 10 ^ { 20 } 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 H i mass of the cloud ( ~ { } \hbox to 0.0 pt { $ > $ } { \lower 4.3 pt \hbox { $ \sim$ } } 2.4 ~ { } M _ { \odot } ) and the blueshift of its mean velocity relative to X Her are inconsistent with an origin tied directly to ejection from the star .