Promising unprecedented convenience, Online Ride Hailing (ORH) service such as Uber and Didi has gained increasing popularity. Different from traditional taxi service, this new on-demand transportation service allows users to request rides from the online service providers at the touch of their fingers. Despite such great convenience, existing ORH systems require the users to expose their locations when requesting rides - a severe privacy issue in the face of untrusted or compromised service providers. In this paper, we propose a private yet efficient ride request scheme, allowing the user to enjoy public ORH service without sacrificing privacy. Unlike previous works, we consider a more practical setting where the information about the drivers and road networks is public. This poses an open challenge to achieve strong security and high efficiency for the secure ORH service. Our main leverage in addressing this problem is hardware-enforced Trusted Execution Environment, in particular Intel SGX enclave. However, the use of secure enclave does not lead to an immediate solution due to the hardware's inherent resource constraint and security limitation. To tackle the limited enclave space, we first design an efficient ride-matching algorithm utilizing hub-based labeling technique, which avoids loading massive road network data into enclave during online processing. To defend against side-channel attacks, we take the next step to make the ride-matching algorithm data-oblivious, by augmenting it with oblivious label access and oblivious distance computation. The proposed solution provides high efficiency of real-time response and strong security guarantee of data-obliviousness. We implement a prototype system of the proposed scheme and thoroughly evaluate it from both theoretical and experimental aspects. The results show that the proposed scheme permits accurate and real-time ride-matching with provable security.