Counterfactual examples are useful for exploring the decision boundaries of machine learning models and determining feature attributions. How can we apply counterfactual-based methods to analyze and explain LLMs? We identify the following key challenges. First, the generated textual counterfactuals should be meaningful and readable to users and thus can be mentally compared to draw conclusions. Second, to make the solution scalable to long-form text, users should be equipped with tools to create batches of counterfactuals from perturbations at various granularity levels and interactively analyze the results. In this paper, we tackle the above challenges and contribute 1) a novel algorithm for generating batches of complete and meaningful textual counterfactuals by removing and replacing text segments in different granularities, and 2) LLM Analyzer, an interactive visualization tool to help users understand an LLM's behaviors by interactively inspecting and aggregating meaningful counterfactuals. We evaluate the proposed algorithm by the grammatical correctness of its generated counterfactuals using 1,000 samples from medical, legal, finance, education, and news datasets. In our experiments, 97.2% of the counterfactuals are grammatically correct. Through a use case, user studies, and feedback from experts, we demonstrate the usefulness and usability of the proposed interactive visualization tool.