As the demand for long-context large language models (LLMs) increases, models with context windows of up to 128k or 256k tokens are becoming increasingly prevalent. However, long-context LLM inference is challenging since the inference speed decreases significantly as the sequence length grows. This slowdown is primarily caused by loading a large KV cache during self-attention. Previous works have shown that a small portion of critical tokens will dominate the attention outcomes. However, we observe the criticality of a token highly depends on the query. To this end, we propose Quest, a query-aware token criticality estimation algorithm. Quest keeps track of the minimal and maximal Key values in KV cache pages and estimates the criticality of a given page using Query vectors. By only loading the Top-K critical KV cache pages for attention, Quest significantly speeds up self-attention without sacrificing accuracy. We show that Quest can achieve up to 6.98x self-attention speedup, which reduces inference latency by 2.27x while performing well on tasks with long dependencies with negligible accuracy loss.