We report the discovery of a z = 2.65 low-ionization iron broad absorption line quasar, FIRST J100424.9+122922, which is gravitationally lensed by a galaxy at z ≈ 0.95. The object was discovered as part of a program to find very red quasars by matching the FIRST radio survey with the Two Micron All Sky Survey in the near-infrared. J100424.9+122922 is the second lensed system to be found in this program, suggesting that many gravitational lenses are probably missed from conventional optical quasar surveys. We have made a simple lens model and a rough estimate of the reddening in the immediate environment of the quasar which suggests that the quasar is intrinsically very luminous and is accreting at close to the Eddington limit of its ~109 M⊙ black hole. The lensing galaxy has a small amount of dust, which is responsible for some excess reddening observed in the fainter image of the quasar, but is otherwise a fairly typical massive elliptical galaxy. We model the selection effects working against the detection of red quasars in both lensed and unlensed samples. We show that these selection effects are very effective at removing even lightly reddened high-redshift quasars from magnitude-limited samples, whether they are lensed or not. This suggests that the red quasar population in general could be very large, and in particular the class of iron broad absorption line quasars of which J100424.9+122922 is a member may be much larger than their rarity in magnitude-limited samples would suggest.
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