In recent years, blockchain-based cloud storage systems have seen rapid development. However, existing systems lack a crucial feature: keyword search, primarily due to file encryption. To address this limitation while maintaining privacy, significant research attention has turned to blockchain-based symmetric searchable encryption (SSE) schemes. However, achieving service fairness in the blockchain security model poses challenges, particularly in ensuring security for both users and service providers, while both can be malicious. To address this challenge, this paper introduces SEARCHAIN, a novel blockchain-based SSE system. We introduce a new role in the scenario, verifier, for the blockchain nodes. With the assistance of honest verifiers, service fairness can be guaranteed. We propose a novel committee selection algorithm for the system to select verifier committee members, ensuring their voting powers are proportional to the number of active SSE services they manage. Verifiers are required to perform result verification work for SSE services to participate in mining. With this approach, the committee selection algorithm provides both security and incentives for the system. We implement a prototype of SEARCHAIN and deploy the system to a local test network. The experimental results demonstrate the feasibility and efficiency of SEARCHAIN.