Echoing the history of search engines and social media content rankings, the advent of large language models (LLMs) has led to a push for increased personalization of model outputs to individual users. In the past, personalized recommendations and ranking systems have been linked to the development of filter bubbles (serving content that may confirm a user's existing biases) and affective polarization (strong negative sentiment towards those with differing views). In this work, we explore how prompting a leading large language model, ChatGPT-3.5, with a user's political affiliation prior to asking factual questions about public figures and organizations leads to differing results. We observe that left-leaning users tend to receive more positive statements about left-leaning political figures and media outlets, while right-leaning users see more positive statements about right-leaning entities. This pattern holds across presidential candidates, members of the U.S. Senate, and media organizations with ratings from AllSides. When qualitatively evaluating some of these outputs, there is evidence that particular facts are included or excluded based on the user's political affiliation. These results illustrate that personalizing LLMs based on user demographics carry the same risks of affective polarization and filter bubbles that have been seen in other personalized internet technologies. This ``failure mode" should be monitored closely as there are more attempts to monetize and personalize these models.