Separation of competing speech is a key challenge in signal processing and a feat routinely performed by the human auditory brain. A long standing benchmark of the spectrogram approach to source separation is known as the ideal binary mask. Here, we train a convolutional deep neural network, on a two-speaker cocktail party problem, to make probabilistic predictions about binary masks. Our results approach ideal binary mask performance, illustrating that relatively simple deep neural networks are capable of robust binary mask prediction. We also illustrate the trade-off between prediction statistics and separation quality.