We have used the Very Large Array to search for neutral atomic hydrogen (H i) in the circumstellar envelopes of five asymptotic giant branch stars. We have detected H i 21 cm emission coincident in both position and velocity with the S-type semiregular variable star RS Cnc. The emission comprises a compact, slightly elongated feature centered on the star with a mean diameter of $82 00 (1:5 ; 10 17 cm), plus an additional filament extending $6 0 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 H i % 1:5 ; 10 À3 M and a mass-loss rateṀ % 1:7 ; 10 À7 M yr À1 . Toward three other stars (IRC+10216, EP Aqr, R Cas) we have detected arcminute-scale H i 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 H i in absorption against the cosmic background previously reported by Le Bertre & Gérard. However, we detect arcs of emission at projected distances of r $ 14 0 Y18 0 ($2 ; 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 H i 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 H i clumps, their inferred H i masses are at least an order of magnitude smaller than their individual gravitational binding masses. We did not detect any H i emission from our fifth target, R Aqr (a symbiotic binary), but measured a 1.4 GHz continuum flux density of 18:8 AE 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.