Edge intelligence (EI), as an emerging technology, has been attracting significant attention. It pushes the frontier of artificial intelligence (AI) from the cloud to the network edge, aiming to embrace and support the next-generation communications while unleashing AI services. However, it faces challenges in its decentralized management and security, which limit its capabilities to support services with numerous requirements. On the other side, blockchain (BC), as a promising decentralized technology, is beneficial to tackle the above issues. However, there exist some technical challenges for BC, such as transaction capacity, scalability, and fault tolerance. Motivated by significant current interest around EI and BC, this survey examines whether the synergy of EI and BC can make a powerful network with combined functionalities of both cutting-edge technologies. Accordingly, we develop EI-chain and Chain-intelligence to realize reliable computing-power management, data administration, and model optimization at the edges, while improving the functions of BC by leveraging complementary characteristics of EI and BC, further making up for their own limitations. In this survey, a wide spectrum of literature is carefully reviewed to enable the EI-chain and Chain-intelligence. Moreover, we cover the technological aspects of EI-chain and Chain-intelligence: overview, motivations, and frameworks. Finally, some challenges and future directions are explored. We believe this survey will provide developers and researchers a comprehensive view on the synergy of EI and BC, while accelerating the design of a powerful integrated network.