We report the observation of synchrony in two unidirectionally coupled (master-slave) model neurons (implemented by electronic circuits) in a noisy environment. Both neurons are subjected to the same random stimulus, and there is a recurrent inhibitory delayed connection in the slave neuron. We observe that synchrony occurs shifted tin time, such that the slave neuron anticipates, i.e., forecasts, the response of the master neuron. By incorporating the effects of unidirectional coupling, delayed feedback and common noise into models of two spiking neurons, we are able to simulate successfully the experimental observations.