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We are constructing a high-performance, special-purpose parallel machine for ab initio Molecular Orbital calculations, called MOE (Molecular Orbital calculation Engine). The sequential execution time is O(N4) where N is the number of basis functions, and most of time is spent to the calculations of electron repulsion integrals (ERIs). The calculation of ERIs have a lot of parallelism of O(N4), and therefore MOE tries to exploit the parallelism. This paper discuss the MOE architecture and examines important aspects of architecture design, which is required to calculate ERIs according to the "Obara method". We conclude that n-way parallelization is the most cost-effective, hence we designed the MOE prototype system with a host computer and many processing nodes. The processing node includes a 76 bit oating-point MULTIPLY-and-ADD unit and internal memory, etc., and it performs ERI computations efficiently. We estimate that the prototype system with 100 processing nodes calculate the energy of proteins in a few days.