Blockchains implement decentralized monetary systems and applications. Recent advancements enable what we call tethering a blockchain to a primary blockchain, securing the tethered chain by nodes that post primary-chain tokens as collateral. The collateral ensures nodes behave as intended, until they withdraw it. Unlike a Proof of Stake blockchain which uses its own token as collateral, using primary-chain tokens shields the tethered chain from the volatility of its own token. State-of-the-art tethered blockchains either rely on centralization, or make extreme assumptions: that all communication is synchronous, that operators remain correct even post-withdrawal, or that withdrawals can be indefinitely delayed by tethered-chain failures. We prove that with partial synchrony, there is no solution to the problem. However, under the standard assumptions that communication with the primary chain is synchronous and communication among the tethered chain nodes is partially synchronous, there is a solution. We present a tethered-chain protocol called Aegis. Aegis uses references from its blocks to primary blocks to define committees, checkpoints on the primary chain to perpetuate decisions, and resets to establish new committees when previous ones become obsolete. It ensures safety at all times and rapid progress when latency among Aegis nodes is low.