Fairness in data mining tasks like clustering has recently become an increasingly important aspect. However, few clustering algorithms exist that focus on fair groupings of data with sensitive attributes. Including fairness in the clustering objective is especially hard for density-based clustering, as it does not directly optimize a closed form objective like centroid-based or spectral methods. This paper introduces FairDen, the first fair, density-based clustering algorithm. We capture the dataset's density-connectivity structure in a similarity matrix that we manipulate to encourage a balanced clustering. In contrast to state-of-the-art, FairDen inherently handles categorical attributes, noise, and data with several sensitive attributes or groups. We show that FairDen finds meaningful and fair clusters in extensive experiments.