Exact diagonalization is a well-established method for simulating small quantum systems. Its applicability is limited by the exponential growth of the so-called Hamiltonian matrix that needs to be diagonalized. Physical symmetries are usually utilized to reduce the matrix dimension, and distributed-memory parallelism is employed to explore larger systems. This paper focuses on the implementation the core distributed algorithms, with a special emphasis on the matrix-vector product operation. Instead of the conventional MPI+X paradigm, Chapel is chosen as the language for these distributed algorithms. We provide a comprehensive description of the algorithms and present performance and scalability tests. Our implementation outperforms the state-of-the-art MPI-based solution by a factor of 7--8 on 32 compute nodes or 4096 cores and exhibits very good scaling on up to 256 nodes or 32768 cores. The implementation has 3 times fewer software lines of code than the current state of the art while remaining fully generic.