To investigate the importance of the Pauli exclusion principle in reactions involving multinucleon systems, the problem of deuteron breakup on a recoilless nucleus is considered. Making some simplifying assumptions, we pose a solvable model problem. Then a Hilbert-Schmidt integral equation is obtained for the breakup amplitude, in which the Pauli term is isolated. Corresponding Pauli breakup cross sections are estimated for a model ${\mathrm{O}}^{16}$ target. Interesting features of energy and angular dependence are discussed.