CRTS J084133.15+200525.8 is an optically bright quasar at z=2.345 that has shown extreme spectral variability over the past decade. Photometrically, the source had a visual magnitude of V~17.3 between 2002 and 2008. Then, over the following five years, the source slowly brightened by approximately one magnitude, to V~16.2. Only ~1 in 10,000 quasars show such extreme variability, as quantified by the extreme parameters derived for this quasar assuming a damped random walk model. A combination of archival and newly acquired spectra reveal the source to be an iron low-ionization broad absorption line (FeLoBAL) quasar with extreme changes in its absorption spectrum. Some absorption features completely disappear over the 9 years of optical spectra, while other features remain essentially unchanged. We report the first definitive redshift for this source, based on the detection of broad H-alpha in a Keck/MOSFIRE spectrum. Absorption systems separated by several 1000 km/s in velocity show coordinated weakening in the depths of their troughs as the continuum flux increases. We interpret the broad absorption line variability to be due to changes in photoionization, rather than due to motion of material along our line of sight. This source highlights one sort of rare transition object that astronomy will now be finding through dedicated time-domain surveys.