''Extreme scattering events'' (ESEs) are attributed to radio wave refr
action by a cloud of free electrons crossing the line of sight. We pre
sent a new model in which these electrons form the photoionized ''skin
'' of an underlying cool, self-gravitating cloud in the Galactic halo.
In this way, we avoid the severe overpressure problem that afflicts o
ther models. The UV flux in the Galactic halo naturally generates elec
tron densities of the right order We demonstrate, for the first time,
a good reproduction of the prototypical ESE in the quasar 0954+658. Th
e neutral clouds are a few astronomical units in radius and have masse
s less than or similar to 10(-3) M.. The observed rate of ESEs implies
that a large fraction of the mass of the Galaxy is in this form.