We present results of electron paramagnetic resonance (EPR) and neutron-diffraction studies of CuCl2·2NC5H5, which is regarded as one of the best known uniform spin-1/2 Heisenberg antiferromagnet chain systems. We reveal that at TN=1.12 K, CuCl2·2NC5H5 undergoes the transition into the magnetically ordered spiral state with Q=(0.5,0.4,0.5) r.l.u. It was shown that the zigzag interchain interactions result in a noticeable geometrical frustration, also affecting the ordered moment per Cu2+ and EPR properties, including the angular dependence of the linewidth. The temperature dependencies of the EPR parameters are discussed.