We have searched for the C-violating decay eta --> gammagammagamma in a sample of similar to 18 million eta mesons produced in phi --> etagamma decays, collected with the KLOE detector at the Frascati phi-factory DAPhiNE. No signal is observed and we obtain the upper limit BR(eta --> gammagammagamma) less than or equal to 1.6 x 10(-5) at 90% CL. (C) 2004 Elsevier B.V. All rights reserved.