  We report the discovery of rapid variations of a high-velocity CIV broad
absorption line trough in the quasar SDSS J141007.74+541203.3. This object was
intensively observed in 2014 as a part of the Sloan Digital Sky Survey
Reverberation Mapping Project, during which 32 epochs of spectroscopy were
obtained with the Baryon Oscillation Spectroscopic Survey spectrograph. We
observe significant (>4sigma) variability in the equivalent width of the broad
(~4000 km/s wide) CIV trough on rest-frame timescales as short as 1.20 days
(~29 hours), the shortest broad absorption line variability timescale yet
reported. The equivalent width varied by ~10% on these short timescales, and by
about a factor of two over the duration of the campaign. We evaluate several
potential causes of the variability, concluding that the most likely cause is a
rapid response to changes in the incident ionizing continuum. If the outflow is
at a radius where the recombination rate is higher than the ionization rate,
the timescale of variability places a lower limit on the density of the
absorbing gas of n_e > 3.9 x 10^5 cm^-3. The broad absorption line variability
characteristics of this quasar are consistent with those observed in previous
studies of quasars, indicating that such short-term variability may in fact be
common and thus can be used to learn about outflow characteristics and
contributions to quasar/host-galaxy feedback scenarios.
