We present the first very long baseline interferometry (VLBI) detections of Zeeman splitting in another galaxy. We used Arecibo Observatory, the Green Bank Telescope, and the Very Long Baseline Array to perform dual-polarization observations of OH maser lines in the merging galaxy Arp 220. We measured magnetic fields of ∼ 1-5 mG associated with three roughly parsec-sized clouds in the nuclear regions of Arp 220. Our measured magnetic fields have comparable strengths and the same direction as features at the same velocity identified in previous Zeeman observations with Arecibo alone. The agreement between single dish and VLBI results provides critical validation of previous Zeeman splitting observations of OH megamasers that used a single large dish. The measured magnetic field strengths indicate that magnetic energy densities are comparable to gravitational energy in OH maser clouds. We also compare our total intensity results to previously published VLBI observations of OH megamasers in Arp 220. We find evidence for changes in both structure and amplitude of the OH maser lines that are most easily explained by variability intrinsic to the masing region, rather than variability produced by interstellar scintillation. Our results demonstrate the potential for using high-sensitivity VLBI to study magnetic fields on small spatial scales in extragalactic systems.