Vehicular Ad Hoc Network (VANET) is a mobile network formed by vehicles, road side units, and other infrastructures that enable communication between the nodes to improve road safety and traffic control. While this technology promises great benefits to drivers, there are many security and privacy concerns that must be addressed before it can be fully adopted. It is essential to ensure that vehicles participating in the network are authenticated and held accountable in case of misbehaviour. On the other hand, there should be adequate mechanisms for preserving the privacy of vehicles and drivers, so they are protected against unauthorized tracking and release of private information. Many current VANET technologies also depend on a central trusted authority that becomes a single point of failure for the network. In this paper, we propose a new blockchain based decentralized authentication approach for VANET. In this scheme vehicles maintain conditional anonymity in the network and their real identities can only be revealed to authorized entities. Using the blockchain technology, we create a distributed framework and maintain an immutable record of the data, strengthening the integrity of the system. We use the Hyperledger Fabric, a permissioned blockchain technology, to implement our approach and compare its performance to the traditional PKI based method for VANET authentication.