Permissionless blockchains offer many advantages but also have significant limitations including high latency. This prevents their use in important scenarios such as retail payments, where merchants should approve payments fast. Prior works have attempted to mitigate this problem by moving transactions off the chain. However, such Layer-2 solutions have their own problems: payment channels require a separate deposit towards each merchant and thus significant locked-in funds from customers; payment hubs require very large operator deposits that depend on the number of customers; and side-chains require trusted validators. In this paper, we propose Snappy, a novel solution that enables recipients, like merchants, to safely accept fast payments. In Snappy, all payments are on the chain, while small customer collaterals and moderate merchant collaterals act as payment guarantees. Besides receiving payments, merchants also act as statekeepers who collectively track and approve incoming payments using majority voting. In case of a double-spending attack, the victim merchant can recover lost funds either from the collateral of the malicious customer or a colluding statekeeper (merchant). Snappy overcomes the main problems of previous solutions: a single customer collateral can be used to shop with many merchants; merchant collaterals are independent of the number of customers; and validators do not have to be trusted. Our Ethereum prototype shows that safe, fast (<2 seconds) and cheap payments are possible on existing blockchains.