With the growing incidents of flash crowds and sophisticated DDoS attacks mimicking benign traffic, it becomes challenging to protect Internet-based services solely by differentiating attack traffic from legitimate traffic. While fair-sharing schemes are commonly suggested as a defense when differentiation is difficult, they alone may suffer from highly variable or even unbounded waiting times. We propose RainCheck Filter (RCF), a lightweight primitive that guarantees bounded waiting time for clients despite server flooding without keeping per-client state on the server. RCF achieves strong waiting time guarantees by prioritizing clients based on how long the clients have waited-as if the server maintained a queue in which the clients lined up waiting for service. To avoid keeping state for every incoming client request, the server sends to the client a raincheck, a timestamped cryptographic token that not only informs the client to retry later but also serves as a proof of the client's priority level within the virtual queue. We prove that every client complying with RCF can access the server in bounded time, even under a flash crowd incident or a DDoS attack. Our large-scale simulations confirm that RCF provides a small and predictable maximum waiting time while existing schemes cannot. To demonstrate its deployability, we implement RCF as a Python module such that web developers can protect a critical server resource by adding only three lines of code.