Counterfactual examples are frequently used for model development and evaluation in many natural language processing (NLP) tasks. Although methods for automated counterfactual generation have been explored, such methods depend on models such as pre-trained language models that are then fine-tuned on auxiliary, often task-specific datasets. Collecting and annotating such datasets for counterfactual generation is labor intensive and therefore, infeasible in practice. Therefore, in this work, we focus on a novel problem setting: \textit{zero-shot counterfactual generation}. To this end, we propose a structured way to utilize large language models (LLMs) as general purpose counterfactual example generators. We hypothesize that the instruction-following and textual understanding capabilities of recent LLMs can be effectively leveraged for generating high quality counterfactuals in a zero-shot manner, without requiring any training or fine-tuning. Through comprehensive experiments on various downstream tasks in natural language processing (NLP), we demonstrate the efficacy of LLMs as zero-shot counterfactual generators in evaluating and explaining black-box NLP models.