Aligning AI systems to users' interests requires understanding and incorporating humans' complex values and preferences. Recently, language models (LMs) have been used to gather information about the preferences of human users. This preference data can be used to fine-tune or guide other LMs and/or AI systems. However, LMs have been shown to struggle with crucial aspects of preference learning: quantifying uncertainty, modeling human mental states, and asking informative questions. These challenges have been addressed in other areas of machine learning, such as Bayesian Optimal Experimental Design (BOED), which focus on designing informative queries within a well-defined feature space. But these methods, in turn, are difficult to scale and apply to real-world problems where simply identifying the relevant features can be difficult. We introduce OPEN (Optimal Preference Elicitation with Natural language) a framework that uses BOED to guide the choice of informative questions and an LM to extract features and translate abstract BOED queries into natural language questions. By combining the flexibility of LMs with the rigor of BOED, OPEN can optimize the informativity of queries while remaining adaptable to real-world domains. In user studies, we find that OPEN outperforms existing LM- and BOED-based methods for preference elicitation.