Paraphrase generation, a crucial task in Natural Language Processing (NLP), is pivotal for the effectiveness of AI chatbots. However, generating high-quality paraphrases that are contextually relevant, semantically equivalent, and linguistically diverse remains a challenge. This paper explores the use of prompt engineering to enhance the paraphrasing capabilities of AI chatbots, specifically focusing on ChatGPT, Bing, and Bard. We introduce a new dataset of 5000 sentences generated by ChatGPT across diverse topics and propose two distinct prompts for paraphrase generation: a direct approach and an engineered prompt. The engineered prompt explicitly instructs the chatbot to generate paraphrases that exhibit lexical diversity, phrasal variations, syntactical differences, fluency, language acceptableness, and relevance, while preserving the original meaning. We conduct a comprehensive evaluation of the generated paraphrases using a range of metrics, including BERTScore, STS-B, METEOR for semantic similarity; ROUGE, BLEU, GLEU for diversity; and CoLA, Perplexity for language acceptableness or fluency. Our findings reveal that the use of the engineered prompt results in higher quality paraphrases across all three chatbots, demonstrating the potential of prompt engineering as a tool for improving chatbot communication.