We have performed wide-field, ultra-low-surface-brightness Hα emission-line mapping around NGC 1068 with the newly commissioned Circumgalactic Hα Spectrograph. NGC 1068 is notable for its active galactic nucleus, which globally ionizes gas in the disk and halo. Line-emitting diffuse ionized gas is distributed throughout the galactic disk and large-scale ionized filaments are found well beyond the disk, aligned with the cone angle of the central jet. We report the discovery of a new ribbon of ionized gas around NGC 1068 beyond even the known outer filamentary structure, located 20 kpc from the galaxy. The Hα surface brightness of this ribbon is on the order of the bright telluric lines, ranging from 4 to 16 R, with fainter regions on the order of the sky background continuum. Unlike previous extended emission, the ribbon is not as well aligned with the current axis of the central jet. It is not associated with any galactic structure or known tidal features in the halo of NGC 1068, though it may originate from a larger distribution of unmapped neutral atomic or molecular gas in the halo. The morphology of the ribbon emission in Hα is correlated with extended UV emission around NGC 1068. Hα-to-UV flux ratios in the ribbon are comparable to extended emission-line ratios in the halos of NGC 5128, NGC 253, and M82. The Hα excess in the ribbon gas suggests ionization by slow shocks or a mixture of in situ star formation and photoionization and collisional ionization processes.