The general solution to the moment-preserving (MP) quantizer problem is presented. It is shown that the moment preserving quantizer is related to the Gauss-Jacobi mechanical quadrature, the output levels of the N-level MP quantizer are the N zeros of an Nth degree orthogonal polynomial associated with the input probability distribution function, and the N-1 thresholds of the MP quantizer are related to the Christoffel numbers through the Chebyshev-Markov-Stieltjes separation theorem. The statistical convergence of the MP quantizer is investigated. MP quantizer tables are presented for the uniform, Gaussian, and Laplacian density functions. The moment-preserving quantizer is shown to be related to block truncation coding. >