  We present an exact ground state solution of a one-dimensional electronic
model for transition-metal oxides in the strong coupling limit. The model
contains doubly degenerated orbit for itinerant electrons and the Hund coupling
between the itinerant electrons and localized spins. The ground state is proven
to be a full ferromagnet for any density of electrons. Our model provides a
rigorous example for metallic ferromagnetism in narrow band systems. The
physical mechanism for ferromagnetism and its relevance to high-dimensional
systems, like R$_{1-x}$X$_x$MnO$_3$, are discussed. Due to the orbital
degeneracy of itinerant electrons, the superexchange coupling can be
ferromagnetic rather than antiferromagnetic in the one-band case.
