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A gauge model with chiral color symmetry of quarks is considered and possibleeffects of the color $G'$-boson octet predicted by this symmetry areinvestigated. The contributions of the $G'$-boson to the cross section$\sigma_{t\bar{t}}$ and to the forward-backward asymmetry $A_{\rm FB}^{p \barp}$ of $t\bar{t}$ production at the Tevatron are calculated and analysed independence on two free parameters of the model, the mixing angle $\theta_G$ and$G'$ mass $m_{G'}$. The $G'$-boson contributions to $\sigma_{t\bar{t}}$ and$A_{\rm FB}^{p \bar p}$ are shown to be consistent with the Tevatron data on$\sigma_{t\bar{t}}$ and $A_{\rm FB}^{p \bar p}$, the allowed region in the$m_{G'} - \theta_G$ plane is discussed and around $m_{G'}=1.2 \, TeV, \;\theta_G=14^\circ $ the region of $1 \sigma$ consistency is found.

Chiral color symmetry and $G'$-boson mass limit from Tevatron data on $t \bar t$-production