Deployed large language models (LLMs) often rely on speculative decoding, a technique that generates and verifies multiple candidate tokens in parallel, to improve throughput and latency. In this work, we reveal a new side-channel whereby input-dependent patterns of correct and incorrect speculations can be inferred by monitoring per-iteration token counts or packet sizes. In evaluations using research prototypes and production-grade vLLM serving frameworks, we show that an adversary monitoring these patterns can fingerprint user queries (from a set of 50 prompts) with over 75% accuracy across four speculative-decoding schemes at temperature 0.3: REST (100%), LADE (91.6%), BiLD (95.2%), and EAGLE (77.6%). Even at temperature 1.0, accuracy remains far above the 2% random baseline - REST (99.6%), LADE (61.2%), BiLD (63.6%), and EAGLE (24%). We also show the capability of the attacker to leak confidential datastore contents used for prediction at rates exceeding 25 tokens/sec. To defend against these, we propose and evaluate a suite of mitigations, including packet padding and iteration-wise token aggregation.