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We present results from spectroscopic observations of AT 2018hyz, a transient discovered by the ASAS-SN survey at an absolute magnitude of $M_V\sim -20.2$ 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 $\sim70-100$ days. 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 AGN in that they show a flat Balmer decrement (H$α$/H$β\sim1.5$), suggesting the lines are collisionally excited rather than being produced via photo-ionisation. The flat Balmer decrement together with the complex profiles suggest 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.