The resolution and the linearity of time measurements made with the CMS electromagnetic calorimeter are studied with samples of data from test beam electrons, cosmic rays, and beam-produced muons. The resulting time resolution measured by lead tungstate crystals is better than 100 ps for energy deposits larger than 10 GeV. Crystal-to-crystal synchronization with a precision of 500 ps is performed using muons produced with the first LHC beams in 2008.