We report on an experimental study of the performance of an electromagnetic calorimeter consisting of thin (0.5 mm diameter) scintillating plastic fibers embedded in lead. Because of the small sampling fraction (3.5% for minimum ionizing particles), this detector is quite compact, with an effective radiation length of 7.2 mm and a Molière radius of 20 mm. Because of the very frequent shower sampling provided by the fibers, the energy resolution is nevertheless good: 9.2%/√E(GeV) for electromagnetic (e.m.) showers, with a small, angle dependent constant term. A non-uniformity in the response is observed at the 2% level across the calorimeter. In spite of the small sampling fraction the light yield is not a limiting factor in this calorimeter: we measured ∼ 500 photoelectrons per GeV shower energy. The position resolution for electrons and two e.m. showers separation have been studied. The fibers sticking out of the back of the detector do not appear to affect the measurements of hadronic showers.