  Random matrix ensembles are introduced that respect the local tensor
structure of Hamiltonians describing a chain of $n$ distinguishable spin-half
particles with nearest-neighbour interactions. We prove a central limit theorem
for the density of states when $n \rightarrow\infty$, giving explicit bounds on
the rate of approach to the limit. Universality within a class of probability
measures and the extension to more general interaction geometries are
established. The level spacing distributions of the Gaussian Orthogonal,
Unitary and Symplectic Ensembles are observed numerically for the energy levels
in these ensembles.
