  The LEP2 data set on the Bhabha process is analyzed with the aim to detect
the signals of the heavy virtual Z' gauge bosons. The state interacting with
the left-handed standard-model doublets and called the Chiral Z' is
investigated. This particle was introduced already as the low-energy state
allowed by the renormalizability of the model. The contribution of the Chiral
Z' state to the Bhabha process is described by two parameters: the coupling to
electrons and the Z-Z' mixing angle. The sign-definite one-parameter observable
is proposed to measure the Z' coupling to the electron current. The
one-parameter fit of the data shows no signals of the particle. The alternative
two-parameter fit of the differential cross-sections is also performed. It also
shows no Chiral Z' signals. The comparisons with other fits are discussed.
