The next generation of vehicles will be autonomous, connected, electric, and intelligent with distinct requirements such as high mobility, low latency, real-time applications, seamless connectivity, and security. Blockchain can provide a good solution to the issue of secure message dissemination or secure information sharing in vehicular networks with a weak trust relationship among the nodes. In this paper, we investigate the design of a regional blockchain for VANETs, where the blockchain is shared among nodes in a geographically bounded area. We investigate how to design the regional blockchain while achieving a low 51% attack success probability. We derive a condition that guarantees a low 51% attack success probability in terms of the numbers of good nodes and malicious nodes, the message delivery time, and the puzzle computation time. The condition can provide a useful guideline for selection of several control parameters guaranteeing the stable operation of the blockchain. We run several simulations to show the validity of the condition and investigate the effects of various parameters on the 51% attack success probability. Our analysis and simulation results show that maintaining a low message delivery time for good nodes is very important in protecting the stability of the blockchain system.