We discuss the sign problem in QCD at nonzero chemical potential and its relation with chiral symmetry breaking and the spectrum of the Dirac operator using the framework of chiral random matrix theory. We show that the Banks--Casher formula is not valid for theories with a sign problem and has to be replaced by an alternative mechanism that is worked out in detail for QCD in one dimension at nonzero chemical potential.

PACS numbers: 11.30.Rd, 12.38.Gc