We report on monitoring of the BL Lac object PKS 2005-489 by the Rossi X-Ra
y Timing Explorer (RXTE) in 1998 October-December. During these months, the
source umderwent a spectacular flare; at its peak on November 10, its 2-10
keV flux was 3.35 x 10(-10) ergs cm(-2) s(-1), over 30 times brighter than
in quiescence. During the rising phase, the X-ray spectrum of PKS 2005-489
hardened considerably, reaching alpha = 1.32 (F-nu proportional to nu(-alp
ha)) near maximum. During the declining phase, the X-ray spectrum steepened
rapidly, reaching alpha = 1.82, then became somewhat harder toward the end
of December (alpha similar to 1.6). While such behavior has been seen befo
re, the simplicity, magnitude, and duration of this flare allowed us to stu
dy it in great detail. We argue that this flare was caused by either the in
jection of particles into the jet or in situ particle acceleration and that
the spectral steepening which followed the flare maximum was the result of
synchrotron cooling. Contrary to other recently observed blazar flares (e.
g., Mrk 501, 3C 279, PKS 2155-304), our results do not imply a major shift
in the location of the synchrotron peak during this flare.