A feasible approach commonly discussed in the literature for mitigating location privacy threats in vehicular ad hoc networks (VANETs) is the use of pseudonyms instead of real vehicle identifications. However, for relevant authorities to be able to identify misbehaving vehicles through their pseudonyms, it is essential that the privacy protection mechanisms only allow for conditional anonymity and not complete anonymity. In this paper, we propose the use of a permissioned consortium blockchain system with smart contract feature to facilitate secure and conditional privacy-preserving vehicular pseudonym issuance and management in a multi-jurisdictional road network. The use of a permissioned consortium blockchain helps mitigate security risks associated with the complexities in interorganizational data handling, such as in the areas of access control, data integrity, confidentiality, and availability. The proposed system architecture takes advantage of the predicted wide availability of Roadside Units (RSUs), and the highly viable, flexible and mature Public Key Infrastructure (PKI) technology for usage in vehicular pseudonymous communications. We successfully carried out a small-scale simulation of the proposed architecture using the Vehicles in Network Simulation (Veins) platform for integrated traffic and network simulation services (SUMO as the traffic simulator and OMNeT++ as the network simulator), and the Hyperledger Fabric platform as the permissioned consortium blockchain system. Simulation and performance analysis results reveal the feasibility of practical deployment of the scheme, and show that the scheme addresses the identified shortfalls of existing works, including the ability to achieve a better balance between connectivity and storage requirements.