We present a Study of exclusive neutral pion production in neutrino-nucleus Neutral Current interactions using data from the NOMAD experiment at the CERN SPS. The data correspond to 1.44 x 10(6) muon-neutrino Charged Current interactions in the energy range 2.5 nu + A + pi(0) and single pi(0) production in neutrino-nucleon scattering. The signature of coherent pi(0) production is an emergent pi(0) almost collinear with the incident neutrino while pi(0)'s produced in neutrino-nucleon deep inelastic scattering have larger transverse momenta. In this analysis all relevant backgrounds to the coherent pi(0) production signal are measured using data themselves. Having determined the backgrounds, and using the Rein-Sehgal model for the coherent pi(0) production to compute the detection efficiency, we obtain 4630 +/- 522(stat) +/- 426(syst) corrected coherent-pi(0) events with E(pi 0) >= 0.5 GeV. We measure sigma(nu A -> nu A pi(0)) = 172.6 +/- 8.1 (stat) +/- 6.9(syst)] x 10(-40) cm(2)/nucleus. This is the most precise measurement of the coherent pi(0) production to date.