Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for 0; we find that quenched QCD is not a simple n0 limit of QCD with n quarks. It is the limit of a theory with 2n quarks: n quarks with original action and n quarks with conjugate action. The results agree with earlier studies of lattice QCD at 0 and provide a simple analytical explanation of a long-standing puzzle.