Conversational search requires accurate interpretation of user intent from complex multi-turn contexts. This paper presents ChatRetriever, which inherits the strong generalization capability of large language models to robustly represent complex conversational sessions for dense retrieval. To achieve this, we propose a simple and effective dual-learning approach that adapts LLM for retrieval via contrastive learning while enhancing the complex session understanding through masked instruction tuning on high-quality conversational instruction tuning data. Extensive experiments on five conversational search benchmarks demonstrate that ChatRetriever substantially outperforms existing conversational dense retrievers, achieving state-of-the-art performance on par with LLM-based rewriting approaches. Furthermore, ChatRetriever exhibits superior robustness in handling diverse conversational contexts. Our work highlights the potential of adapting LLMs for retrieval with complex inputs like conversational search sessions and proposes an effective approach to advance this research direction.