  We analyze 1598 serendipitous Chandra X-ray observations of 462 radio-quiet
quasars to constrain the frequency of extreme amplitude X-ray variability that
is intrinsic to the quasar corona and innermost accretion flow. The quasars in
this investigation are all spectroscopically confirmed, optically bright ($m_i
\leq$ 20.2), and contain no identifiable broad absorption lines in their
optical/ultraviolet spectra. This sample includes quasars spanning $z \approx$
0.1 - 4 and probes X-ray variability on timescales of up to $\approx$ 12
rest-frame years. Variability amplitudes are computed between every epoch of
observation for each quasar and are analyzed as a function of timescale and
luminosity. The tail-heavy distributions of variability amplitudes at all
timescales indicate that extreme X-ray variations are driven by an additional
physical mechanism and not just typical random fluctuations of the coronal
emission. Similarly, extreme X-ray variations of low-luminosity quasars seem to
be driven by an additional physical mechanism, whereas high-luminosity quasars
seem more consistent with random fluctuations. The amplitude at which an X-ray
variability event can be considered extreme is quantified for different
timescales and luminosities. Extreme X-ray variations occur more frequently at
long timescales ( $\Delta t \gtrsim$ 300 days) than at shorter timescales, and
in low-luminosity quasars compared to high-luminosity quasars over a similar
timescale. A binomial analysis indicates that extreme intrinsic X-ray
variations are rare, with a maximum occurrence rate of <2.4% of observations.
Finally, we present X-ray variability and basic optical emission-line
properties of three archival quasars that have been newly discovered to exhibit
extreme X-ray variability.
