Gravitational lens models for the double quasar 0957 + 561 predict that there should be a time delay of roughly 1 year between the arrival of wave fronts from the two images. In order to measure this delay, we have been monitoring the flux densities at lambda = 6 cm of 0957 + 561A and 0957 + 561B since 1979. We present the flux curves of the two images constructed from the VLA data, which are accurate to 2% of the image flux densities. The VLA data are best fitted by a time delay of 1.40 +/- 0.1 yr (513 +/- 40 days, A leading), with a magnification ratio (B/A) of 0.697 +/- 0.003. The error estimates were obtained through Monte Carlo methods, and include 68% of the simulated solutions.