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To determine the dominant sources for cosmic reionization, the evolution history of the global ionizing fraction, and the topology of the ionized regions, we have conducted a deep imaging survey using four narrow-band (NB) and one intermediate-band (IB) filters on the Subaru/Hyper Suprime-Cam (HSC), called Cosmic HydrOgen Reionization Unveiled with Subaru (CHORUS). The central wavelengths and full-widths-at-half-maximum of the CHORUS filters are, respectively, 386.2 nm and 5.5 nm for NB387, 526.0 nm and 7.9 nm for NB527, 717.1 nm and 11.1 nm for NB718, 946.2 nm and 33.0 nm for IB945, and 971.2 nm and 11.2 nm for NB973. This combination, including NB921 (921.5 nm and 13.5 nm) from the Subaru Strategic Program with HSC (HSC SSP), are carefully designed, as if they were playing a chorus, to observe multiple spectral features simultaneously, such as Lyman continuum, Ly$α$, C~{\sc iv}, and He~{\sc ii} for $z=2$--$7$. The observing field is the same as that of the deepest footprint of the HSC SSP in the COSMOS field and its effective area is about 1.6 deg$^2$. Here, we present an overview of the CHORUS project, which includes descriptions of the filter design philosophy, observations and data reduction, multiband photometric catalogs, assessments of the imaging quality, measurements of the number counts, and example use cases of the data. All the imaging data, photometric catalogs, masked pixel images, data of limiting magnitudes and point spread functions, results of completeness simulations, and source number counts are publicly available through the HSC SSP database.