This study investigates whether popular LLMs exhibit bias towards elite universities when generating personas for technology industry professionals. We employed a novel persona-based approach to compare the educational background predictions of GPT-3.5, Gemini, and Claude 3 Sonnet with actual data from LinkedIn. The study focused on various roles at Microsoft, Meta, and Google, including VP Product, Director of Engineering, and Software Engineer. We generated 432 personas across the three LLMs and analyzed the frequency of elite universities (Stanford, MIT, UC Berkeley, and Harvard) in these personas compared to LinkedIn data. Results showed that LLMs significantly overrepresented elite universities, featuring these universities 72.45% of the time, compared to only 8.56% in the actual LinkedIn data. ChatGPT 3.5 exhibited the highest bias, followed by Claude Sonnet 3, while Gemini performed best. This research highlights the need to address educational bias in LLMs and suggests strategies for mitigating such biases in AI-driven recruitment processes.