Smart Grid 3.0 is the latest evolution of the smart grid and incorporates advanced computing and communication technologies. The synchrophasor communication system plays a critical role in wide-area measurement systems (WAMS) for real-time protection and control of power systems, supporting the objectives of Smart Grid 3.0. This system relies on synchrophasor communication technologies, where Phasor Measurement Units (PMUs) transmit synchrophasor data to Phasor Data Concentrators (PDCs) over the synchrophasor communication network. The communication infrastructure of this network is based on the TCP/IP protocol stack, which, unfortunately, is susceptible to cyberattacks, posing security threats such as data tampering and false data injection. These vulnerabilities undermine the intended benefits of synchrophasor applications in terms of situational awareness, observability, grid reliability, resiliency, and synchronized monitoring and control in the smart grid. To address these challenges, it is crucial to enhance the security, integrity, and confidentiality of synchrophasor data within the communication system. This paper proposes a blockchain-based synchrophasor communication system that preserves the security and integrity of synchrophasor data. In this paper, an architecture is proposed for a synchrophasor communication system based on blockchain technology. The proposed architecture aims to enhance the security and integrity of synchrophasor measurements. Furthermore, the architecture is developed as a peer-to-peer distributed blockchain network, leveraging the robustness of a distributed, decentralized, hierarchical PDC architecture. To evaluate the efficacy of the proposed architecture, two case studies, one using the IEEE 9 bus and the other using IEEE 14 bus systems are considered. Moreover, various challenges with potential solutions are also recommended. The proposed work is envisioned to contribute to the advancement of Smart Grid 3.0 by adopting blockchain technology for synchrophasor applications.