The total cross section for gamma p -> 3pi0 p has been measured for the first time from threshold to 1.4 GeV using the tagged photon beam of the Mainz Microtron. The equipment utilized the Crystal Ball multiphoton spectrometer, the TAPS forward detector and a particle identification detector. The gamma p -> 3pi0 p total cross section has two broad enhancements at sqrt{s}~1.5 GeV and 1.7 GeV. We obtained the ratio of the total cross sections gamma p -> 3pi0 p to gamma p -> eta p equal to 0.014 pm 0.001 at sqrt{s}~1.5 GeV.