A novel method for nonlinear prediction of speech is introduced which does not require a parametric model of the predictor. The observable past is vector quantized and a nonlinear prediction is obtained by a table lookup, addressed by the index of the quantized input vector. The table is designed with speech training data. Experimental results for a moving-average process confirm that nearly optimal nonlinear prediction is achievable. Results for speech show that the performance depends on both the size of the vector quantizer codebook and the size of the training set. The method is applied to DPCM and some useful performance gain is demonstrated.