Abstract We report the discovery of two quasars at a redshift of z = 6.05 in the process of merging. They were serendipitously discovered from the deep multiband imaging data collected by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. The quasars, HSC J121503.42−014858.7 (C1) and HSC J121503.55−014859.3 (C2), both have luminous (>1043 erg s−1) Lyα emission with a clear broad component (full width at half maximum >1000 km s−1). The rest-frame ultraviolet (UV) absolute magnitudes are M 1450 = − 23.106 ± 0.017 (C1) and −22.662 ± 0.024 (C2). Our crude estimates of the black hole masses provide log ( M BH / M ⊙ ) = 8.1 ± 0.3 in both sources. The two quasars are separated by 12 kpc in projected proper distance, bridged by a structure in the rest-UV light suggesting that they are undergoing a merger. This pair is one of the most distant merging quasars reported to date, providing crucial insight into galaxy and black hole build-up in the hierarchical structure formation scenario. A companion paper will present the gas and dust properties captured by Atacama Large Millimeter/submillimeter Array observations, which provide additional evidence for and detailed measurements of the merger, and also demonstrate that the two sources are not gravitationally lensed images of a single quasar.