Query auto-completion (QAC) is one of the most prominent features of modern search engines. The list of query candidates is generated according to the prefix entered by the user in the search box and is updated on each new key stroke. Query prefixes tend to be short and ambiguous, and existing models mostly rely on the past popularity of matching candidates for ranking. However, the popularity of certain queries may vary drastically across different demographics and users. For instance, while instagram and imdb have comparable popularities overall and are both legitimate candidates to show for prefix i, the former is noticeably more popular among young female users, and the latter is more likely to be issued by men. In this paper, we present a supervised framework for personalizing auto-completion ranking. We introduce a novel labelling strategy for generating offline training labels that can be used for learning personalized rankers. We compare the effectiveness of several user-specific and demographic-based features and show that among them, the user’s long-term search history and location are the most effective for personalizing auto-completion rankers. We perform our experiments on the publicly available AOL query logs, and also on the larger-scale logs of Bing. The results suggest that supervised rankers enhanced by personalization features can significantly outperform the existing popularity-based base-lines, in terms of mean reciprocal rank (MRR) by up to 9%.