Fairness and Outlier Detection (OD) are closely related, as it is exactly the goal of OD to spot rare, minority samples in a given population. When being a minority (as defined by protected variables, e.g. race/ethnicity/sex/age) does not reflect positive-class membership (e.g. criminal/fraud), however, OD produces unjust outcomes. Surprisingly, fairness-aware OD has been almost untouched in prior work, as fair machine learning literature mainly focus on supervised settings. Our work aims to bridge this gap. Specifically, we develop desiderata capturing well-motivated fairness criteria for OD, and systematically formalize the fair OD problem. Further, guided by our desiderata, we propose FairOD, a fairness-aware outlier detector, which has the following, desirable properties: FairOD (1) does not employ disparate treatment at test time, (2) aims to flag equal proportions of samples from all groups (i.e. obtain group fairness, via statistical parity), and (3) strives to flag truly high-risk fraction of samples within each group. Extensive experiments on a diverse set of synthetic and real world datasets show that FairOD produces outcomes that are fair with respect to protected variables, while performing comparable to (and in some cases, even better than) fairness-agnostic detectors in terms of detection performance.