There is increased interest in smart vehicles acting as both data consumers and producers in smart cities. Vehicles can use smart city data for decision-making, such as dynamic routing based on traffic conditions. Moreover, the multitude of embedded sensors in vehicles can collectively produce a rich data set of the urban landscape that can be used to provide a range of services. Key to the success of this vision is a scalable and private architecture for trusted data sharing. This paper proposes a framework called SpeedyChain, that leverages blockchain technology to allow smart vehicles to share their data while maintaining privacy, integrity, resilience and non- repudiation in a decentralized, and tamper-resistant manner. Differently from traditional blockchain usage (e.g., Bitcoin and Ethereum), the proposed framework uses a blockchain design that decouples the data stored in the transactions from the block header, thus allowing for fast addition of data to the blocks. Furthermore, an expiration time for each block to avoid large sized blocks is proposed. This paper also presents an evaluation of the proposed framework in a network emulator to demonstrate its benefits.