DNNs are known to be vulnerable to so-called adversarial attacks, in which inputs are carefully manipulated to induce misclassification. Existing defenses are mostly software-based and come with high overheads or other limitations. This paper presents HASI, a hardware-accelerated defense that uses a process we call stochastic inference to detect adversarial inputs. HASI carefully injects noise into the model at inference time and used the model's response to differentiate adversarial inputs from benign ones. We show an adversarial detection rate of average 87% which exceeds the detection rate of the state-of-the-art approaches, with a much lower overhead. We demonstrate a software/hardware-accelerated co-design, which reduces the performance impact of stochastic inference to 1.58X-2X relative to the unprotected baseline, compared to 14X-20X overhead for a software-only GPU implementation.