The candidate chiral doublet bands in ${}^{128}$La have been searched for through the ${}^{118}$Sn(${}^{14}$N, 4n)${}^{128}$La reaction at a beam energy of 69 MeV. A positive-parity sideband with the same configuration as that of the yrast band has been identified. The positive-parity and spins of the sideband have been assigned based on the $\ensuremath{\Delta}I=1$ mixed $M1/E2$ and $E2$ characters of the linking transitions between the sideband and the yrast band. The properties of the sideband and the yrast band are discussed. The newly identified sideband and the yrast band are suggested to form the candidate of the near degenerate chiral doublet bands.