Data-driven methodologies offer many exciting upsides, but they also introduce new challenges, particularly in the realm of user privacy. Specifically, the way data is collected can pose privacy risks to end users. In many routing services, a single entity (e.g., the routing service provider) collects and manages user trajectory data. When it comes to user privacy, these systems have a central point of failure since users have to trust that this entity will not sell or use their data to infer sensitive private information. Unfortunately, in practice many advertising companies offer to buy such data for the sake of targeted advertisements. With this as motivation, we study the problem of using location data for routing services in a privacy-preserving way. Rather than having users report their location to a central operator, we present a protocol in which users participate in a decentralized and privacy-preserving computation to estimate travel times for the roads in the network in a way that no individuals' location is ever observed by any other party. The protocol uses the Laplace mechanism in conjunction with secure multi-party computation to ensure that it is cryptogrpahically secure and that its output is differentially private. A natural question is if privacy necessitates degradation in accuracy or system performance. We show that if a road has sufficiently high capacity, then the travel time estimated by our protocol is provably close to the ground truth travel time. We validate the protocol through numerical experiments which show that using the protocol as a routing service provides privacy guarantees with minimal overhead to user travel time.