We observe Bose–Einstein correlations in π0 pairs using back-to-back two jet hadronic events from Z0 decays in the data sample collected by the OPAL detector at LEP 1 from 1991 to 1995. Using a static Gaussian picture for the pion emitter source, we obtain the chaoticity parameter λ=0.55±0.10±0.10 and the source radius R=(0.59±0.08±0.05) fm. According to the JETSET and HERWIG Monte Carlo models, the Bose–Einstein correlations in our data sample largely connect π0s originating from the decays of different hadrons. Prompt pions formed at string break-ups or cluster decays only form a small fraction of the sample.