  A black hole-like solution to a toy model scalar field action for the pion is
presented. It has a "horizon" that traps pion field information (it cannot
escape in finite time) and is thermal, with a finite and calculable
temperature, $T=\sqrt{2}/(\pi\alpha)$, with $\alpha$ a coupling parameter. The
action is a scalar DBI action (D-brane action), coupled to a particular fixed
source term. The DBI action by itself has "catenoid" solutions that have
horizons with infinite temperature and trap only high energy information. It is
also proven that the unique scalar action that admits thermal horizons is of
DBI type at leading order, making the D-brane action special. The existence of
this "pionless hole" solution means that {\em aparent} information loss is not
a feature of gravity theories (via black holes), but even a simple scalar
theory can exhibit it. This is as it should, since the "pionless hole" is a toy
model for the AdS-CFT dual to a black hole.
