A method is herein proposed and demonstrated for the space-time optimization of monitoring networks for groundwater quality. The objective is to provide a minimum cost design algorithm that will assist in determining where and when to sample existing wells dedicated to defining, through periodic sampling, the behavior of groundwater contaminants. The method has three characteristics: (1) The combined spatial and temporal redundancy of the sampling network is considered by using a Kalman filter coupled with a stochastic transport model in which velocity and dispersion are spatially correlated random fields. (2) The sampling network is optimized using an enumerative method that minimizes a function of the estimate variance. (3) A real-time update of the estimate is obtained using again the Kalman filter. The synthetic examples presented show that for a contaminant plume in motion this method can obtain cost-effective sampling networks.