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We use a random matrix model to study chiral symmetry breaking in QCD atfinite chemical potential $\mu$. We solve the model and compute the eigenvaluedensity of the Dirac matrix on a complex plane. A naive ``replica trick'' failsfor $\mu\neq0$: we find that quenched QCD is not a simple $n\to0$ limit of QCDwith $n$ quarks. It is the limit of a theory with $2n$ quarks: $n$ quarks withoriginal action and $n$ quarks with conjugate action. The results agree withearlier studies of lattice QCD at $\mu\neq0$ and provide a simple analyticalexplanation of a long-standing puzzle.Comment: 9 pages, revtex3.0, 4 epsf figures. Packed by "uufiles" script.  Revised version (PRL): minor change

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