  We report a deep search for HI 21cm emission from the $z= 0.00632$ sub-DLA
toward PG1216+069 with the Giant Metrewave Radio Telescope. No emission was
detected and our $5\sigma$ upper limit on the mass of any associated galaxy is
$M_{\rm HI} \lesssim 10^7 M_\odot$, nearly 3 orders of magnitude less than
M$_{\rm HI}^\star$. The $z \sim 0.006$ absorber is thus the most extreme known
deviation from the standard paradigm in which high column density quasar
absorption lines arise in the disks of gas-rich galaxies.
