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I report the discovery of blueshifted broad absorption line (BAL) troughs inat least six transitions of the Balmer series of hydrogen (Hbeta to H9) and inCaII, MgII and excited FeII in the quasar SDSS J125942.80+121312.6. This isonly the fourth active galactic nucleus known to exhibit Balmer absorption, allfour in conjunction with low-ionization BAL systems containing excited Fe II.The substantial population in the n=2 shell of H I in this quasar's absorberlikely arises from Ly-alpha trapping. In an absorber sufficiently opticallythick to show Balmer absorption, soft X-rays from the quasar penetrate to large\tau_Ly\alpha and ionize H I. Recombination then creates Ly-alpha photons thatincrease the n=2 population by a factor \tau_Ly\alpha since they require about\tau_Ly\alpha scatterings to diffuse out of the absorber. Observing Ly-alphatrapping in a quasar absorber requires a large but Compton-thin column of gasalong our line of sight which includes substantial H I but not too much dust.Presumably the rarity of Balmer-line BAL troughs reflects the rarity of suchconditions in quasar absorbers.Comment: AJ in press. 4 pages, 1 figure, 1 table, emulateapj forma

A Quasar with Broad Absorption in the Balmer Lines