The deep learning revolution has been enabled in large part by GPUs, and more recently accelerators, which make it possible to carry out computationally demanding training and inference in acceptable times. As the size of machine learning networks and workloads continues to increase, multi-GPU machines have emerged as an important platform offered on High Performance Computing and cloud data centers. As these machines are shared between multiple users, it becomes increasingly important to protect applications against potential attacks. In this paper, we explore the vulnerability of Nvidia's DGX multi-GPU machines to covert and side channel attacks. These machines consist of a number of discrete GPUs that are interconnected through a combination of custom interconnect (NVLink) and PCIe connections. We reverse engineer the cache hierarchy and show that it is possible for an attacker on one GPU to cause contention on the L2 cache of another GPU. We use this observation to first develop a covert channel attack across two GPUs, achieving the best bandwidth of 3.95 MB/s. We also develop a prime and probe attack on a remote GPU allowing an attacker to recover the cache hit and miss behavior of another workload. This basic capability can be used in any number of side channel attacks: we demonstrate a proof of concept attack that fingerprints the application running on the remote GPU, with high accuracy. Our work establishes for the first time the vulnerability of these machines to microarchitectural attacks, and we hope that it guides future research to improve their security.