Algorithmic racism refers to instances of racism resulting from computational systems. Researchers such as Noble (2018) and Broussard (2023) have documented causes of algorithmic racism caused by various computational devices, from search engine algorithms to racial profiling in distinct databases. As a result, developing methodological tools to enhance algorithmic fairness and mitigate racial bias in these systems has become a central focus of AI governance and AI ethics. The chapter aims to introduce the problem of establishing effective governance and ethical guidelines for improving algorithmic fairness in Large Language Models (LLMs), drawing on the audit models discussed by J. Mökander and L. Floridi (2021) and focusing on how instances of algorithmic racism may occur in LLMs. The central purpose is to introduce and discuss ethical and epistemic desiderata for evaluating how Large Language Models and other AI chatbots understand and potentially perpetuate racial discrimination.