We present the first observation of quantum interference in the process phi -> KSKL -> pi(+)pi(-)pi(+)pi(-), using the KLOE detector at the Frascati e(+)e(-) collider DA Phi NE. From about 5 x 10(4) neutral kaon pairs both decaying to pi(+)pi(-) pairs we obtain the distribution of At,. the difference between the two kaon decay times, which allows testing the validity of quantum mechanics and C P T invariance: no violation of either is observed. New or improved limits on coherence loss and C P T violation are presented. (c) 2006 Elsevier B.V. All rights reserved.