Visualization recommendation work has focused solely on scoring visualizations based on the underlying dataset and not the actual user and their past visualization feedback. These systems recommend the same visualizations for every user, despite that the underlying user interests, intent, and visualization preferences are likely to be fundamentally different, yet vitally important. In this work, we formally introduce the problem of personalized visualization recommendation and present a generic learning framework for solving it. In particular, we focus on recommending visualizations personalized for each individual user based on their past visualization interactions (e.g., viewed, clicked, manually created) along with the data from those visualizations. More importantly, the framework can learn from visualizations relevant to other users, even if the visualizations are generated from completely different datasets. Experiments demonstrate the effectiveness of the approach as it leads to higher quality visualization recommendations tailored to the specific user intent and preferences. To support research on this new problem, we release our user-centric visualization corpus consisting of 17.4k users exploring 94k datasets with 2.3 million attributes and 32k user-generated visualizations.