For workloads operating on sensitive user data, privacy loss should be carefully orchestrated to enforce a global bound on personal data leakage. This paper presented PrivateKube, an extension to the Kubernetes workload orchestrator that adds differential privacy budget as a new native resource to be managed alongside traditional compute resources. PrivateKube incorporates a novel scheduling algorithm, DPF, the first one suitable for the unique characteristics of the privacy resource, including its all-or-nothing utility and non-replenishable nature. We show that DPF has desirable theoretical properties, outperforms baseline scheduling algorithms, and that native integration of privacy into Kubernetes can facilitate reuse of existing tools to better manage this scarce resource.