We report on the discovery of a peculiar broad absorption line (BAL) quasar identified in our Gaia-assisted survey of red quasars. The systemic redshift of this quasar was difficult to establish because of the absence of conspicuous emission lines. Based on deep and broad BAL troughs of at least Six202f;IV, Cx202f;IV, and Alx202f;III, a redshift of zx2004;=& x2004;2.41 was established under the assumption that the systemic redshift can be inferred from the red edge of the BAL troughs. However, we observe a weak and spatially extended emission line at 4450 angstrom that is most likely due to Lyman-alpha emission, which implies a systemic redshift of zx2004;=x2004;2.66 if correctly identified. There is also evidence for the onset of Lyman-alpha forest absorption bluewards of 4450 angstrom and evidence for H alpha emission in the K band consistent with a systemic redshift of zx2004;=& x2004;2.66. If this redshift is correct, the quasar is an extreme example of a detached low-ionisation BAL quasar. The BALs must originate from material moving with very large velocities ranging from 22 000 km s(-1) to 40 000 km s(-1). To our knowledge, this is the first case of a systemic-redshift measurement based on extended Lyman-alpha emission for a BAL quasar. This method could also be useful in cases of sufficiently distant BL Lac quasars without systemic-redshift information.