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We explore the use of large language models (LLMs) for zero-shot semantic parsing. Semantic parsing involves mapping natural language utterances to task-specific meaning representations. Language models are generally trained on the publicly available text and code and cannot be expected to directly generalize to domain-specific parsing tasks in a zero-shot setting. In this work, we propose ZEROTOP, a zero-shot task-oriented parsing method that decomposes a semantic parsing problem into a set of abstractive and extractive question-answering (QA) problems, enabling us to leverage the ability of LLMs to zero-shot answer reading comprehension questions. For each utterance, we prompt the LLM with questions corresponding to its top-level intent and a set of slots and use the LLM generations to construct the target meaning representation. We observe that current LLMs fail to detect unanswerable questions; and as a result, cannot handle questions corresponding to missing slots. To address this problem, we fine-tune a language model on public QA datasets using synthetic negative samples. Experimental results show that our QA-based decomposition paired with the fine-tuned LLM can correctly parse ~16% of utterances in the MTOP dataset without requiring any annotated data.