An outlier detection method may be considered fair over specified sensitive attributes if the results of outlier detection are not skewed towards particular groups defined on such sensitive attributes. In this task, we consider, for the first time to our best knowledge, the task of fair outlier detection. In this work, we consider the task of fair outlier detection over multiple multi-valued sensitive attributes (e.g., gender, race, religion, nationality, marital status etc.). We propose a fair outlier detection method, FairLOF, that is inspired by the popular LOF formulation for neighborhood-based outlier detection. We outline ways in which unfairness could be induced within LOF and develop three heuristic principles to enhance fairness, which form the basis of the FairLOF method. Being a novel task, we develop an evaluation framework for fair outlier detection, and use that to benchmark FairLOF on quality and fairness of results. Through an extensive empirical evaluation over real-world datasets, we illustrate that FairLOF is able to achieve significant improvements in fairness at sometimes marginal degradations on result quality as measured against the fairness-agnostic LOF method.