We present the first experimental evidence for Andreev reflection in a
single-electron transistor with both the leads and the island superco
nducting, In this process, two electrons tunnel to form a Cooper pair,
or the reverse. It provides a second mechanism for two-electron trans
fer in addition to Cooper pair tunneling. Andreev reflection is found
to contribute to several current cycles within the Coulomb blockade of
single-electron tunneling. The observation of these cycles, however,
requires that the charging energy E-C<Delta.