The desire and ability to seek new information strategically are fundamental to human learning but often overlooked in current language agent development. Using a web shopping task as an example, we show that it can be reformulated and solved as a retrieval task without a requirement of interactive information seeking. We then redesign the task to introduce a new role of shopper, serving as a realistically constrained communication channel. The agents in our proposed ChatShop task explore user preferences in open-ended conversation to make informed decisions. Our experiments demonstrate that the proposed task can effectively evaluate the agent's ability to explore and gradually accumulate information through multi-turn interaction. We also show that LLM-simulated shoppers serve as a good proxy to real human shoppers and discover similar error patterns of agents.