We are developing a liquid xenon calorimeter for the MEG experiment. This experiment, to be performed at the Paul Scherrer Institut (PSI) in Villigen (CH), was designed by an Italian-Japanese-Russian-Swiss collaboration to search for the μ+→e+γ decay, forbidden in the Standard Model of Electro-Weak and Strong Interactions. The photon four momentum is to be measured by an innovative C-shaped 800 litres liquid xenon calorimeter read by more than 800 photo-multiplier tubes. An absorption length for Xe scintillation light larger than 100 cm has been measured. The performance of such a detector has been measured using a large volume prototype (100 litres) in a test beam at PSI, using high energy photons from decays of neutral pions from a charge exchange reaction of negative pions on protons. A resolution of 5% FWHM was obtained.