Recently, a new acoustic model based on deep neural networks (DNN) has been introduced. While the DNN has generated significant improvements over GMM based systems on several tasks, there has been no evaluation of the robustness of such systems to environmental distortion. In this paper, we investigate the noise robustness of DNN based acoustic models and find that they can match state-of-the-art performance on the Aurora 4 task without any explicit noise compensation. This performance can be further improved by incorporating information about the environment into DNN training using a new method called noise-aware training. When combined with the recently proposed dropout training technique, a 7.5% relative improvement over the previously best published result on this task is achieved using only a single decoding pass and no additional decoding complexity compared to a standard DNN.