  Recent dynamical studies indicate that the possibility of an Earth-like
planet around $\alpha\;$Cen A or B should be taken seriously. Such a planet, if
it exists, would perturb the orbital astrometry by $<10 \ {\mu}\rm as$, which
is $10^{-6}$ of the separation between the two stars. We assess the feasibility
of detecting such perturbations using ground-based intensity interferometry. We
simulate a dedicated setup consisting of four 40-cm telescopes equipped with
photon counters and correlators with time resolution $0.1\,\rm ns$, and a sort
of matched filter implemented through an aperture mask. The astrometric error
from one night of observing $\alpha\;$Cen AB is $\approx0.5\,\rm mas$. The
error decreases if longer observing times and multiple spectral channels are
used, as $(\hbox{channels}\times\hbox{nights})^{-1/2}$.
