A parallel version of D. Neuhauser's filter diagonalization algorithm is presented. In contrast to the usual procedure of acting with a set of narrow filter operators on a single or just a few initial vectors, parallelizability is achieved by working with a single, broad filter operator and a correspondingly large number of initial vectors. Apart from the obvious speedup in computation time, there is no need for communication between the processors involved in the computation. Furthermore, because a significantly reduced number of matrix vector multiplications is needed per initial vector, parallel filter diagonalization is numerically more stable than the single processor approach. It is argued that this method is particularly attractive for calculating eigenvectors of the large-scale secular matrices arising in quantum chemistry, especially in dense spectral regions. An application to dense state distributions of a cationic molecular cluster serves as an illustrative example. This is the first time filter diagonalization is used as a tool for ab initio electronic structure calculations.