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Most permissionless blockchain networks run on peer-to-peer (P2P) networks, which offer flexibility and decentralization at the expense of performance (e.g., network latency). Historically, this tradeoff has not been a bottleneck for most blockchains. However, an emerging host of blockchain-based applications (e.g., decentralized finance) are increasingly sensitive to latency; users who can reduce their network latency relative to other users can accrue (sometimes significant) financial gains. In this work, we initiate the study of strategic latency reduction in blockchain P2P networks. We first define two classes of latency that are of interest in blockchain applications. We then show empirically that a strategic agent who controls only their local peering decisions can manipulate both types of latency, achieving 60% of the global latency gains provided by the centralized, paid service bloXroute, or, in targeted scenarios, comparable gains. Finally, we show that our results are not due to the poor design of existing P2P networks. Under a simple network model, we theoretically prove that an adversary can always manipulate the P2P network's latency to their advantage, provided the network experiences sufficient peer churn and transaction activity.