Requirements Elicitation (RE) is a crucial software engineering skill that involves interviewing a client and then devising a software design based on the interview results. Teaching this inherently experiential skill effectively has high cost, such as acquiring an industry partner to interview, or training course staff or other students to play the role of a client. As a result, a typical instructional approach is to provide students with transcripts of real or fictitious interviews to analyze, which exercises the skill of extracting technical requirements but fails to develop the equally important interview skill itself. As an alternative, we propose conditioning a large language model to play the role of the client during a chat-based interview. We perform a between-subjects study (n=120) in which students construct a high-level application design from either an interactive LLM-backed interview session or an existing interview transcript describing the same business processes. We evaluate our approach using both a qualitative survey and quantitative observations about participants' work. We find that both approaches provide sufficient information for participants to construct technically sound solutions and require comparable time on task, but the LLM-based approach is preferred by most participants. Importantly, we observe that LLM-backed interview is seen as both more realistic and more engaging, despite the LLM occasionally providing imprecise or contradictory information. These results, combined with the wide accessibility of LLMs, suggest a new way to practice critical RE skills in a scalable and realistic manner without the overhead of arranging live interviews.