  A gauge model with chiral color symmetry is considered and possible effects
of the color $G'$-boson octet predicted by this symmetry are investigated in
dependence on two free parameters, the mixing angle $\theta_G$ and $G'$ mass
$m_{G'}$. The allowed region in the $m_{G'} - \theta_G$ plane is found from the
Tevatron data on the cross section $\sigma_{t\bar{t}}$ and forward-backward
asymmetry $A_{\rm FB}^{p \bar p}$ of the $t\bar{t}$ production. The mass limits
for the $G'$-boson are shown to be stronger than those for the axigluon. A
possible effect of the $G'$-boson on the $t\bar{t}$ production at the LHC is
discussed and the mass limits providing for the $G'$-boson evidence at the LHC
are estimated in dependence on $\theta_G$.
