Microarchitectural side channels are a pressing security threat. These channels are created when programs modulate hardware resources in a secret data-dependent fashion. They are broadly classified as being either stateful or stateless (also known as contention-based), depending on whether they leave behind a trace for attackers to later observe. Common wisdom suggests that stateful channels are significantly easier to monitor than stateless ones, and hence have received the most attention. In this paper, we present a novel stateless attack that shows this common wisdom is not always true. Our attack, called Binoculars, exploits unexplored interactions between in-flight page walk operations and other memory operations. Unlike other stateless channels, Binoculars creates significant timing perturbations-up to 20,000 cycles stemming from a single dynamic instruction-making it easy to monitor. We show how these perturbations are address dependent, enabling Binoculars to leak more virtual address bits in victim memory operations than any prior channel. Binoculars needs no shared memory between the attacker and the victim. Using Binoculars, we design both covert- and side-channel attacks. Our covert channel achieves a high capacity of 1116 KB/s on a Cascade Lake-X machine. We then design a side-channel attack that steals keys from OpenSSL's side-channel resistant ECDSA by learning the ECDSA nonce k. Binoculars' ability to significantly amplify subtle behaviors, e.g., orderings of stores, is crucial for this attack to succeed because the nonce changes after each run. Finally, we fully break kernel ASLR.