Stock market prices are known to be very volatile and noisy, and their accurate forecasting is a challenging problem. Traditionally, both linear and non-linear methods (such as ARIMA and LSTM) have been proposed and successfully applied to stock market prediction, but there is room to develop models that further reduce the forecast error. In this paper, we introduce a Deep Convolutional Generative Adversarial Network (DCGAN) architecture to deal with the problem of forecasting the closing price of stocks. To test the empirical performance of our proposed model we use the FTSE MIB (Financial Times Stock Exchange Milano Indice di Borsa), the benchmark stock market index for the Italian national stock exchange. By conducting both single-step and multi-step forecasting, we observe that our proposed model performs better than standard widely used tools, suggesting that Deep Learning (and in particular GANs) is a promising field for financial time series forecasting.