First measurements of cross sections for isolated prompt photon production in deep inelastic ep scattering have been made using the ZEUS detector at the HERA electron-proton collider using an integrated luminosity of 121 pb(-1). A signal for isolated photons in the transverse energy and rapidity ranges 5 < E-T(y) < 10 GeV and -0.7 < eta(gamma) < 0.9 was observed for virtualities of T the exchanged photon of Q(2) > 35 GeV2. Cross sections are presented for inclusive prompt photons and for those accompanied by a single jet in the range E-jet(T) greater than or equal to 6 GeV and 1.5 less than or equal to eta(jet) < 1.8. Calculations at order alpha(3)alpha(s), describe the data reasonably well. (C) 2004 Elsevier B.V. All rights reserved.