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