  The contributions of $G'$-boson predicted by the chiral color symmetry of
quarks to the charge asymmetry $A_C(p p \to t\bar{t})$ in $t \bar{t}$
production at the LHC and to the forward-backward asymmetry $A_{\rm
FB}(p\bar{p} \to t\bar{t})$ in $t\bar{t}$ production at the Tevatron are
calculated and analysed in dependence on two free parameters of the model, the
$G'$ mass $m_{G'}$ and mixing angle $\theta_G$. The $m_{G'} - \theta_G$ regions
of $1 \sigma$ consistency with the CMS data on the cross section $\sigma(pp \to
t\bar{t})$ and on the charge asymmetry $A_C(p p \to t\bar{t})$ are found and
compared with those resulted from the CDF data on the cross section
$\sigma(p\bar{p} \to t\bar{t})$ and on the forward-backward asymmetry $A_{\rm
FB}(p\bar{p} \to t\bar{t})$ of $t \bar{t}$ production at the Tevatron with
account of the current SM predictions for $A_{\rm FB}(p\bar{p} \to t\bar{t})$.
