Visual tracking is fundamentally the problem of regressing the state of the target in each video frame. While significant progress has been achieved, trackers are still prone to failures and inaccuracies. It is therefore crucial to represent the uncertainty in the target estimation. Although current prominent paradigms rely on estimating a state-dependent confidence score, this value lacks a clear probabilistic interpretation, complicating its use. In this work, we therefore propose a probabilistic regression formulation and apply it to tracking. Our network predicts the conditional probability density of the target state given an input image. Crucially, our formulation is capable of modeling label noise stemming from inaccurate annotations and ambiguities in the task. The regression network is trained by minimizing the Kullback-Leibler divergence. When applied for tracking, our formulation not only allows a probabilistic representation of the output, but also substantially improves the performance. Our tracker sets a new state-of-the-art on six datasets, achieving 59.8% AUC on LaSOT and 75.8% Success on TrackingNet.