  We report the detection of an HI counterpart to the extended,
far-ultraviolet-emitting tail associated with the asymptotic giant branch star
Mira (o Ceti). Using the Nancay Radio Telescope (NRT), we have detected
emission as far as 88' north of the star, confirming that the tail contains a
significant atomic component (M_HI ~ 4x10e-3 M_sun). The NRT spectra reveal a
deceleration of the tail gas caused by interaction with the local interstellar
medium. We estimate an age for the tail of ~1.2x10e5 years, suggesting that the
mass-loss history of Mira has been more prolonged than previous observational
estimates. Using the Very Large Array (VLA) we have also imaged the HI tail out
to ~12' (0.4 pc) from the star. The detected emission shows a ``head-tail''
morphology, but with complex substructure. Regions with detected HI emission
correlate with far-ultraviolet-luminous regions on large scales, but the two
tracers are not closely correlated on smaller scales (<1'). We propose that
detectable tails of HI are likely to be a common feature of red giants
undergoing mass-loss.
