Extending large language models (LLMs) to process longer inputs is crucial for numerous applications. However, the considerable computational cost of transformers, coupled with limited generalization of positional encoding, restricts the size of their context window. We introduce Cross-Attention to Parallel Encodings (CAPE), a framework that can be applied to any existing decoder-only LLMs for context expansion. CAPE leverages a small encoder to process a long input chunk by chunk and enables the frozen decoder to cross-attend to the additional contexts. CAPE is efficient, generalizable, and versatile: trained with 8K-token documents, CAPE extends the context window of LLaMA-2 to 128K tokens, offering $10\times$ of the throughput with only 1/6 of the memory. CAPE yields strong performance on language modeling and in-context learning. CAPE also excels in retrieval-augmented applications, while existing long-context models degenerate with retrieved contexts. We further introduce a CAPE variant that can extend the context window of instruction-tuned models with only unlabeled data, and showcase its effectiveness on LLaMA-2-Chat, leading to a strong instruction-following model that can leverage very long context on downstream tasks.