Outside the highly publicized victories in the game of Go, there have been numerous successful applications of deep learning in the fields of information retrieval, computer vision, and speech recognition. In cybersecurity, an increasing number of companies have begun exploring the use of deep learning (DL) in a variety of security tasks with malware detection among the more popular. These companies claim that deep neural networks (DNNs) could help turn the tide in the war against malware infection. However, DNNs are vulnerable to adversarial samples, a shortcoming that plagues most, if not all, statistical and machine learning models. Recent research has demonstrated that those with malicious intent can easily circumvent deep learning-powered malware detection by exploiting this weakness. To address this problem, previous work developed defense mechanisms that are based on augmenting training data or enhancing model complexity. However, after analyzing DNN susceptibility to adversarial samples, we discover that the current defense mechanisms are limited and, more importantly, cannot provide theoretical guarantees of robustness against adversarial sampled-based attacks. As such, we propose a new adversary resistant technique that obstructs attackers from constructing impactful adversarial samples by randomly nullifying features within data vectors. Our proposed technique is evaluated on a real world dataset with 14,679 malware variants and 17,399 benign programs. We theoretically validate the robustness of our technique, and empirically show that our technique significantly boosts DNN robustness to adversarial samples while maintaining high accuracy in classification. To demonstrate the general applicability of our proposed method, we also conduct experiments using the MNIST and CIFAR-10 datasets, widely used in image recognition research.