We report the discovery of Balmer broad absorption lines (BALs) in the quasar LBQS 1206+1052 and present a detailed analysis of the peculiar absorption line spectrum. Besides Mg II doublet, BALs are also detected in He I* multiplet at \AA arising from metastable helium level, and in H and H from excited hydrogen H I* level, which are rarely seen in quasar spectra. We identify two components in the BAL troughs of 2000 km s width: One component shows an identical profile in H I*, \hei* and \mgii with its centroid blueshifted by km\ s. The other component is detected in \hei* and \mgii with km s. We estimate the column densities of H I*, He I*, and Mg II, and compare them with possible level population mechanisms. Our results favor the scenario that the Balmer BALs originate in a partially ionized region with a column density of cm for an electron density of $n_e\sim 10^{6-8} ^{-3}\alpha$ resonant scattering pumping. The harsh conditions needed may help to explain the rarity of Balmer absorption line systems in quasar spectra. With an -band PSF magnitude of 16.50, LBQS 1206+1052 is the brightest Balmer-BAL quasar ever reported. Its high brightness and unique spectral properties make LBQS 1206+1052 a promising candidate for follow-up high-resolution spectroscopy, multi-band observations, and long-term monitoring.

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