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Clients of permissionless blockchain systems, like Bitcoin, rely on an underlying peer-to-peer network to send and receive transactions. It is critical that a client is connected to at least one honest peer, as otherwise the client can be convinced to accept a maliciously forked view of the blockchain. In such an eclipse attack, the client is unable to reliably distinguish the canonical view of the blockchain from the view provided by the attacker. The consequences of this can be catastrophic if the client makes business decisions based on a distorted view of the blockchain transactions. In this paper, we investigate the design space and propose two approaches for Bitcoin clients to detect whether an eclipse attack against them is ongoing. Each approach chooses a different trade-off between average attack detection time and network load. The first scheme is based on the detection of suspicious block timestamps. The second scheme allows blockchain clients to utilize their natural connections to the Internet (i.e., standard web activity) to gossip about their blockchain views with contacted servers and their other clients. Our proposals improve upon previously proposed eclipse attack countermeasures without introducing any dedicated infrastructure or changes to the Bitcoin protocol and network, and we discuss an implementation. We demonstrate the effectiveness of the gossip-based schemes through rigorous analysis using original Internet traffic traces and real-world deployment. The results indicate that our protocol incurs a negligible overhead and detects eclipse attacks rapidly with high probability, and is well-suited for practical deployment.