We establish the existence of strongly localized wave packets tracing
without dispersion the classical dynamics of a Rydberg electron in a c
ircularly polarized microwave field over up to 10(6) periods of the dr
iving field, which at the same time are single eigenstates of the atom
dressed by the microwave field. These single-state wave packets are s
hown to be robust towards small changes of the external field and can
be prepared experimentally.