Memory bottlenecks severely constrain the deployment of large language models (LLMs) in long-context scenarios. While existing global pruning methods reduce memory usage during the decoding phase, they largely ignore out-of-memory errors in the prefill stage before generation begins. To address this, we present Task-Aware Chunked KV Cache Eviction (TAKE), a training-free framework for memory-efficient long-context prefill. TAKE refines the prefill process by partitioning long sequences into chunks and performing incremental KV eviction, thereby avoiding the computational overhead of full-sequence processing. Crucially, to mitigate the semantic discontinuity introduced by chunk-wise processing, we introduce accumulated task-aware probe tokens and a delayed eviction strategy to reduce information loss. Extensive evaluations show that TAKE achieves the highest efficiency, slashing peak memory usage to 59.53% of the baseline while accelerating Time-To-First-Token (TTFT) by over 60% under 128k-token inference. Our code is available at [Source Code of TAKE](https://github.com/ObitoJN/TAKE).