We present results from spectroscopic observations of AT 2018hyz, a transient discovered by the All-Sky Automated Survey for Supernova survey at an absolute magnitude of M-V similar to -20.2 mag, in the nucleus of a quiescent galaxy with strong Balmer absorption lines. AT 2018hyz shows a blue spectral continuum and broad emission lines, consistent with previous TDE candidates. High cadence follow-up spectra show broad Balmer lines and He I in early spectra, with He II making an appearance after similar to 70-100 d. The Balmer lines evolve from a smooth broad profile, through a boxy, asymmetric double-peaked phase consistent with accretion disc emission, and back to smooth at late times. The Balmer lines are unlike typical active galactic nucleus in that they show a flat Balmer decrement (H alpha/H beta similar to 1.5), suggesting the lines are collisionally excited rather than being produced via photoionization. The flat Balmer decrement together with the complex profiles suggests that the emission lines originate in a disc chromosphere, analogous to those seen in cataclysmic variables. The low optical depth of material due to a possible partial disruption may be what allows us to observe these double-peaked, collisionally excited lines. The late appearance of He II may be due to an expanding photosphere or outflow, or late-time shocks in debris collisions.