A measurement of direct photon production in 208Pb+208Pb collisions at 158A GeV has been carried out in the CERN WA98 experiment. The invariant yield of direct photons in central collisions is extracted as a function of transverse momentum in the interval 0.5<p(T)<4 GeV/c. A significant direct photon signal, compared to statistical and systematical errors, is seen at p(T)>1.5 GeV/c. The result constitutes the first observation of direct photons in ultrarelativistic heavy-ion collisions. It could be significant for diagnosis of quark-gluon-plasma formation.