As artificial intelligence (AI) tools become widely adopted, large language models (LLMs) are increasingly involved on both sides of decision-making processes, ranging from hiring to content moderation. This dual adoption raises a critical question: do LLMs systematically favor content that resembles their own outputs? Prior research in computer science has identified self-preference bias -- the tendency of LLMs to favor their own generated content -- but its real-world implications have not been empirically evaluated. We focus on the hiring context, where job applicants often rely on LLMs to refine resumes, while employers deploy them to screen those same resumes. Using a large-scale controlled resume correspondence experiment, we find that LLMs consistently prefer resumes generated by themselves over those written by humans or produced by alternative models, even when content quality is controlled. The bias against human-written resumes is particularly substantial, with self-preference bias ranging from 67% to 82% across major commercial and open-source models. To assess labor market impact, we simulate realistic hiring pipelines across 24 occupations. These simulations show that candidates using the same LLM as the evaluator are 23% to 60% more likely to be shortlisted than equally qualified applicants submitting human-written resumes, with the largest disadvantages observed in business-related fields such as sales and accounting. We further demonstrate that this bias can be reduced by more than 50% through simple interventions targeting LLMs' self-recognition capabilities. These findings highlight an emerging but previously overlooked risk in AI-assisted decision making and call for expanded frameworks of AI fairness that address not only demographic-based disparities, but also biases in AI-AI interactions.