  In models involving new TeV-scale Z' gauge bosons, the new U(1)' symmetry
often prevents the generation of Majorana masses needed for a conventional
neutrino seesaw, leading to three super-weakly interacting right-handed
neutrinos, the Dirac partners of the ordinary neutrinos. These can be produced
prior to Big Bang Nucleosynthesis (BBN) by the Z' interactions, leading to a
faster expansion rate and too much ^4He. We quantify the constraints on the Z'
properties from nucleosynthesis for Z' couplings motivated by a class of E6
models parametrized by an angle theta_E6. The decoupling temperature, which is
higher than that of ordinary left-handed neutrinos due to the large Z' mass, is
calculated, and the equivalent number of extra weakly interacting neutrinos,
Delta N_nu, is obtained numerically as a function of the Z' mass, couplings,
and the Z-Z' mixing angle. The ^4He abundance from BBN gives the most stringent
limit on M_Z' unless Z' coupling to the right-handed neutrinos are small.
