  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
multi-band imaging data collected by the Hyper Suprime-Cam (HSC) Subaru
Strategic Program survey. The quasars, HSC $J$121503.42$-$014858.7 (C1) and HSC
$J$121503.55$-$014859.3 (C2), both have luminous ($>$10$^{43}$ erg s$^{-1}$)
Ly$\alpha$ emission with a clear broad component (full width at half maximum
$>$1000 km s$^{-1}$). The rest-frame ultraviolet (UV) absolute magnitudes are
$M_{1450} = -23.106 \pm 0.017$ (C1) and $-22.662 \pm 0.024$ (C2). Our crude
estimates of the black hole masses provide $\log (M_{\rm BH}/M_\odot) = 8.1 \pm
0.3$ 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.
