Public blockchains impose an inherent tension between regulatory compliance and user privacy. Existing on-chain identity solutions require centralized KYC attestors, specialized hardware, or Decentralized Identifier (DID) frameworks needing entirely new credential infrastructure. Meanwhile, over four billion active X.509 certificates constitute a globally deployed, government-grade trust infrastructure largely unexploited for decentralized identity. This paper presents zk-X509, a privacy-preserving identity system bridging legacy Public Key Infrastructure (PKI) with public ledgers via a RISC-V zero-knowledge virtual machine (zkVM). Users prove ownership of standard X.509 certificates without revealing private keys or personal identifiers. Crucially, the private key never enters the ZK circuit; ownership is proven via OS keychain signature delegation (macOS Security.framework, Windows CNG). The circuit verifies certificate chain validity, temporal validity, key ownership, trustless CRL revocation, blockchain address binding, and Sybil-resistant nullifier generation. It commits 13 public values, including a Certificate Authority (CA) Merkle root hiding the issuing CA, and four selective disclosure hashes. We formalize eight security properties under a Dolev-Yao adversary with game-based definitions and reductions to sEUF-CMA, SHA-256 collision resistance, and ZK soundness. Evaluated on the SP1 zkVM, the system achieves 11.8M cycles for ECDSA P-256 (17.4M for RSA-2048), with on-chain Groth16 verification costing ~300K gas. By leveraging certificates deployed at scale across jurisdictions, zk-X509 enables adoption without new trust establishment, complementing emerging DID-based systems.