  We present a spin-1 chain with a Hamiltonian which has three exactly solvable
ground states. Two of these are fully dimerized, analogous to the
Majumdar-Ghosh (MG) states of a spin-1/2 chain, while the third is of the
Affleck-Kennedy-Lieb-Tasaki (AKLT) type. We use variational and numerical
methods to study the low-energy excitations which interpolate between these
ground states in different ways. In particular, there is a spin-1/2 excitation
which interpolates between the MG and AKLT ground states; this is the lowest
excitation of the system and it has a surprisingly small gap. We discuss
generalizations of our model of spin fractionalization to higher spin chains
and higher dimensions.
