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We present the first experimental search for the rare charm decay D0→π0ν¯ν. It is based on an e+e− collision sample consisting of 10.6×10^6 pairs of D0¯D0 mesons collected by the BESIII detector at √s=3.773 GeV, corresponding to an integrated luminosity of 2.93 fb^−1. A data-driven method is used to ensure the reliability of the background modeling. No significant D0→π0ν¯ν signal is observed in data and an upper limit of the branching fraction is set to be 2.1×10^-4 at the 90% confidence level. This is the first experimental constraint on charmed-hadron decays into dineutrino final states.