  Gamma rays at rest frame energies as high as 90 GeV have been reported from
gamma-ray bursts (GRBs) by the Fermi Large Area Telescope (LAT). There is
considerable hope that a confirmed GRB detection will be possible with the
upcoming Cherenkov Telescope Array (CTA), which will have a larger effective
area and better low-energy sensitivity than current-generation imaging
atmospheric Cherenkov telescopes (IACTs). To estimate the likelihood of such a
detection, we have developed a phenomenological model for GRB emission between
1 GeV and 1 TeV that is motivated by the high-energy GRB detections of
Fermi-LAT, and allows us to extrapolate the statistics of GRBs seen by lower
energy instruments such as the Swift-BAT and BATSE on the Compton Gamma-ray
Observatory. We show a number of statistics for detected GRBs, and describe how
the detectability of GRBs with CTA could vary based on a number of parameters,
such as the typical observation delay between the burst onset and the start of
ground observations. We also consider the possibility of using GBM on Fermi as
a finder of GRBs for rapid ground follow-up. While the uncertainty of GBM
localization is problematic, the small field-of-view for IACTs can potentially
be overcome by scanning over the GBM error region. Overall, our results
indicate that CTA should be able to detect one GRB every 20 to 30 months with
our baseline instrument model, assuming consistently rapid pursuit of GRB
alerts, and provided that spectral breaks below 100 GeV are not a common
feature of the bright GRB population. With a more optimistic instrument model,
the detection rate can be as high as 1 to 2 GRBs per year.
