A search for the decay mu -> e gamma, performed at PSI and based on data from the initial three months of operation of the MEG experiment, yields an upper limit on the branching ratio of BR(mu -> e gamma) < 2.8 x 10**-11 (90% C.L.). This corresponds to the measurement of positrons and photons from ~ 10**14 stopped mu-decays by means of a superconducting positron spectrometer and a 900 litre liquid xenon photon detector.