We have used the Very Large Array ( VLA ) to search for neutral atomic hydrogen ( \HI ) in the circumstellar envelopes of five asymptotic giant branch ( AGB ) stars . We have detected \HI 21-cm emission coincident in both position and velocity with the S-type semi-regular variable star RS Cnc . The emission comprises a compact , slightly elongated feature centered on the star with a mean diameter of \sim 82 ^ { \prime \prime } ( 1.5 \times 10 ^ { 17 } cm ) , plus an additional filament extending \sim 6 ^ { \prime } to the northwest . If this filament is associated with RS Cnc , it would imply that a portion of its mass-loss is highly asymmetric . We estimate M _ { HI } \approx 1.5 \times 10 ^ { -3 } M _ { \odot } and a mass-loss rate { \dot { M } } \approx 1.7 \times 10 ^ { -7 } M _ { \odot } yr ^ { -1 } . Toward three other stars ( IRC+10216 , EP Aqr , R Cas ) , we have detected arcminute-scale \HI emission features at velocities consistent with the circumstellar envelopes , but spatially offset from the stellar positions . Toward R Cas , the emission is weak but peaks at the stellar systemic velocity and overlaps with the location of its circumstellar dust shell and thus is probably related to the star . In the case of IRC+10216 , we were unable to confirm the detection of \HI in absorption against the cosmic background previously reported by Le Bertre & Gérard . However , we detect arcs of emission at projected distances of r \sim 14 ^ { \prime } -18 ^ { \prime } ( \sim 2 \times 10 ^ { 18 } cm ) to the northwest of the star . The large separation of the emission from the star is plausible given its advanced evolutionary status , although it is unclear if the asymmetric distribution and complex velocity structure are consistent with a circumstellar origin . For EP Aqr , the detected \HI emission comprises multiple clumps redward of the systemic velocity , but we are unable to determine unambiguously whether the emission arises from the circumstellar envelope or from interstellar clouds along the line-of-sight . Regardless of the adopted distance for the \HI clumps , their inferred \HI masses are at least an order of magnitude smaller than their individual gravitational binding masses . We did not detect any \HI emission from our fifth target , R Aqr ( a symbiotic binary ) , but measured a 1.4 GHz continuum flux density of 18.8 \pm 0.7 mJy . R Aqr is a previously known radio source , and the 1.4 GHz emission likely arises primarily from free-free emission from an ionized circumbinary envelope .