  We study the spectral properties of a chiral random banded matrix (chRBM)
with elements decaying as a power-law ${{\cal H}_{ij}}\sim |i-j|^{-\alpha}$.
This model is equivalent to a chiral 1D Anderson Hamiltonian with long range
power-law hopping. In the weak disorder limit we obtain explicit
nonperturbative analytical results for the density of states and the two-level
correlation function by mapping the chRBM onto a nonlinear sigma model. We also
put forward, by exploiting the relation between the chRBM at $\alpha=1$ and a
generalized chiral random matrix model, an exact expression for the above
correlation functions. We give compelling analytical and numerical evidence
that for this value the chRBM reproduces all the features of an Anderson
transition. Finally we discuss possible applications of our results to QCD.
