  We report the discovery of the first brown dwarf binary system with a Y dwarf
primary, WISE J033605.05$-$014350.4, observed with NIRCam on JWST with the
F150W and F480M filters. We employed an empirical point spread function binary
model to identify the companion, located at a projected separation of 84
milliarcseconds, position angle of 295 degrees, and with contrast of 2.8 and
1.8 magnitudes in F150W and F480M, respectively. At a distance of 10$\,$pc
based on its Spitzer parallax, and assuming a random inclination distribution,
the physical separation is approximately 1$\,$au. Evolutionary models predict
for that an age of 1-5 Gyr, the companion mass is about 4-12.5 Jupiter masses
around the 7.5-20 Jupiter mass primary, corresponding to a companion-to-host
mass fraction of $q=0.61\pm0.05$. Under the assumption of a Keplerian orbit the
period for this extreme binary is in the range of 5-9 years. The system joins a
small but growing sample of ultracool dwarf binaries with effective
temperatures of a few hundreds of Kelvin. Brown dwarf binaries lie at the nexus
of importance for understanding the formation mechanisms of these elusive
objects, as they allow us to investigate whether the companions formed as stars
or as planets in a disk around the primary.
