  The birth of gravitational-wave / electromagnetic astronomy was heralded by
the joint observation of gravitational waves (GWs) from a binary neutron star
(BNS) merger by Advanced LIGO and Advanced Virgo, GW170817, and of gamma-rays
from the short gamma-ray burst GRB170817A by the Fermi Gamma-ray Burst Monitor
(GBM) and INTEGRAL. This detection provided the first direct evidence that at
least a fraction of BNSs are progenitors of short GRBs. GRBs are now also known
to emit very-high-energy (VHE, > 100 GeV) photons as has been shown by recent
independent detections of the GRBs 1901114C and 180720B by the ground-based
gamma-ray detectors MAGIC and H.E.S.S. In the next years, the Cherenkov
Telescope Array (CTA) will boost the searches for VHE counterparts thanks to
its unprecedented sensitivity, rapid response and capability to monitor large
sky areas via survey-mode operation. In this contribution, we present the CTA
program of observations following the detection of GW events. We discuss
various follow-up strategies and links to multi-wavelength and multi-messenger
observations. Finally we outline the capabilities and prospects of detecting
VHE emission from GW counterparts.
