  On the basis of existing observations (at the 4.5 \sigma level) of TeV
gamma-ray outbursts from the Fanaroff-Riley I (FRI) radio galaxy Centaurus A,
we estimate the accompanying neutrino flux in a scenario where both photons and
neutrinos emerge from pion decay. We find a neutrino flux on Earth
dF_{\nu}/dE_\nu = 4.5\times 10^{-11} (E_\nu/TeV)^{-2} TeV^{-1} cm^{-2} s^{-1},
equally spread in flavor as a result of maximal mixing. Such a flux will
trigger at the IceCube facility about 10 showers/burst, with negligible
background from atmospheric muons, and primary neutrino energies in excess of
100 TeV. The only other FRI radio galaxy observed in the TeV photon energy
range at the 4\sigma level is M87. The burst nature of this activity is not
established; however, we show that the intrinsic neutrino luminosity during the
active period is the same as the Centaurus A burst. On the assumption that
Centaurus A typifies the FRI population, we show that IceCube should collect 10
showers (all neutrino flavors) in 3 years, attaining a 95% CL sensitivity to
the diffuse neutrino flux from FRI radio galaxies in one year of observation.
