With the rise of digital currency systems that rely on blockchain to ensure ledger security, the ability to perform cross-chain transactions is becoming a crucial interoperability requirement. Such transactions allow not only funds to be transferred from one blockchain to another (as done in atomic swaps), but also a blockchain to verify the inclusion of any event on another blockchain. Cross-chain bridges are protocols that allow on-chain exchange of cryptocurrencies, on-chain transfer of assets to sidechains, and cross-shard verification of events in sharded blockchains, many of which rely on Byzantine fault tolerance (BFT) for scalability. Unfortunately, existing bridge protocols that can transfer funds from a BFT blockchain incur significant computation overhead on the destination blockchain, resulting in a high gas cost for smart contract verification of events. In this paper, we propose Horizon, a gas-efficient, cross-chain bridge protocol to transfer assets from a BFT blockchain to another blockchain (e.g., Ethereum) that supports basic smart contract execution.