Large Language Models are increasingly employed in generating consumer product recommendations, yet their potential for embedding and amplifying gender and race biases remains underexplored. This paper serves as one of the first attempts to examine these biases within LLM-generated recommendations. We leverage prompt engineering to elicit product suggestions from LLMs for various race and gender groups and employ three analytical methods-Marked Words, Support Vector Machines, and Jensen-Shannon Divergence-to identify and quantify biases. Our findings reveal significant disparities in the recommendations for demographic groups, underscoring the need for more equitable LLM recommendation systems.