Using data collected with the BESIII detector operating at the Beijing Electron Positron Collider at center-of-mass energies of sqrt[s]=4.23, 4.26, and 4.36 GeV, we observe e(+)e(-)→π(0)π(0)hc for the first time. The Born cross sections are measured and found to be about half of those of e(+)e(-)→π(+)π(-)hc within less than 2σ. In the π(0)hc mass spectrum, a structure at 4.02 GeV/c(2) is found. It is most likely to be the neutral isospin partner of the Zc(4020)(±) observed in the process of e(+)e(-)→π(+)π(-)hc being found. A fit to the π(0)hc invariant mass spectrum, with the width of the Zc(4020)(0) fixed to that of its charged isospin partner and possible interferences with non-Zc(4020)(0) amplitudes neglected, gives a mass of (4023.9±2.2±3.8) MeV/c(2) for the Zc(4020)(0), where the first error is statistical and the second systematic.