In this paper, we describe the optical imaging data processing pipeline developed for the Subaru Telescopes Hyper Suprime-Cam (HSC) instrument. The HSC Pipeline builds on the prototype pipeline being developed by the Large Synoptic Survey Telescopes Data Management system, adding customizations for HSC, large-scale processing capabilities, and novel algorithms that have since been reincorporated into the LSST codebase. While designed primarily to reduce HSC Subaru Strategic Program (SSP) data, it is also the recommended pipeline for reducing general-observer HSC data. The HSC pipeline includes high level processing steps that generate coadded images and science-ready catalogs as well as low-level detrending and image characterizations.