  We report the discovery of a close quasar pair candidate at $z=5.66$,
J2037--4537. J2037--4537 is resolved into two quasar images at the same
redshift in ground-based observations. Followup spectroscopy shows significant
differences in both the continuum slopes and emission line properties of the
two images. The two quasar images have a projected separation of $1\farcs24$
($7.3\text{~kpc}$ at $z=5.66$) and a redshift difference of $\Delta
z\lesssim0.01$. High-resolution images taken by {\em Hubble Space Telescope} do
not detect the foreground lensing galaxy. The observational features of
J2037--4537 strongly disfavor the lensing hypothesis. If J2037--4537 is a
physical quasar pair, it indicates a quasar clustering signal of $\sim10^5$ at
a separation of $\sim10$ proper kpc (pkpc), and gives the first observational
constraint on the pair fraction of $z>5$ quasars,
$f_\text{pair}(r<30\text{~pkpc})>0.3\%$. The properties of J2037--4537 are
consistent with those of merger-triggered quasar pairs in hydrodynamical
simulations of galaxy mergers.

Astrophysics of Galaxies