A Candidate Kiloparsec-scale Quasar Pair at $z=5.66$

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.