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The LEP2 data set on the Bhabha process is analyzed with the aim to detectthe signals of the heavy virtual Z' gauge bosons. The state interacting withthe left-handed standard-model doublets and called the Chiral Z' isinvestigated. This particle was introduced already as the low-energy stateallowed by the renormalizability of the model. The contribution of the ChiralZ' state to the Bhabha process is described by two parameters: the coupling toelectrons and the Z-Z' mixing angle. The sign-definite one-parameter observableis proposed to measure the Z' coupling to the electron current. Theone-parameter fit of the data shows no signals of the particle. The alternativetwo-parameter fit of the differential cross-sections is also performed. It alsoshows no Chiral Z' signals. The comparisons with other fits are discussed.Comment: 15 pages, 4 figures. The paper was completely rewritten on the base  of new dat

Signals of Z′ boson in the Bhabha process within the LEP2 data set