  We consider two particles hopping on a chain with a contact interaction
between them. At strong interaction, there is a molecular bound state separated
by a direct gap from a continuous band of atomic states. Introducing weak
disorder in the interaction, the molecular state becomes Anderson localized. At
stronger disorder, part of the molecular band delocalizes and dissociates due
to its hybridization to the atomic band. We characterize these different
regimes by computing the density of states, the inverse participation ratio,
the level-spacing statistics and the survival probability of an initially
localized state. The atomic band is best described as that of a rough billiard
for a single particle on a square lattice that shows signatures of quantum
chaos. In addition to typical "chaotic states", we find states that are
localized along only one direction. These "separatrix states" are more
localized than chaotic states, and similar in this respect to scarred states,
but their existence is due to the separatrix iso-energy line in the
interaction-free dispersion relation, rather than to unstable periodic orbits.
