Trellis-coded quantization is generalized to allow a vector reproduction alphabet. Three encoding structures are described, several encoder design rules are presented, and two design algorithms are developed. It is shown that for a stationary, ergodic vector source, if the optimized trellis-coded vector quantization reproduction process is jointly stationary and ergodic with the source, then the quantization noise is zero-mean and of variance equal to the difference between the source variance and the variance of the reproduction sequence. Several examples illustrate the encoder design procedure and performance.