  We study the Kondo effect generated by a single magnetic impurity embedded in
an ultrasmall metallic grain, to be called a ``Kondo box''. We find that the
Kondo resonance is strongly affected when the mean level spacing in the grain
becomes larger than the Kondo temperature, in a way that depends on the parity
of the number of electrons on the grain. We show that the single-electron
tunneling conductance through such a grain features Kondo-induced Fano-type
resonances of measurable size, with an anomalous dependence on temperature and
level spacing.
