Recent advances in Deep Neural Networks (DNN) and Edge Computing have made it possible to automatically analyze streams of videos from home/security cameras over hierarchical clusters that include edge devices, close to the video source, as well as remote cloud compute resources. However, preserving the privacy and confidentiality of users' sensitive data as it passes through different devices remains a concern to most users. Private user data is subject to attacks by malicious attackers or misuse by internal administrators who may use the data in activities that are not explicitly approved by the user. To address this challenge, we present Serdab, a distributed orchestration framework for deploying deep neural network computation across multiple secure enclaves (e.g., Intel SGX). Secure enclaves provide a guarantee on the privacy of the data/code deployed inside it. However, their limited hardware resources make them inefficient when solely running an entire deep neural network. To bridge this gap, Serdab presents a DNN partitioning strategy to distribute the layers of the neural network across multiple enclave devices or across an enclave device and other hardware accelerators. Our partitioning strategy achieves up to 4.7x speedup compared to executing the entire neural network in one enclave.