Using time-resolved 1s-2p excitonic Lyman spectroscopy, we study the orthoexciton-to-paraexciton transfer, following the creation of a high density population of ultracold 1s orthoexcitons by resonant two-photon excitation with femtosecond pulses. An observed fast exciton-density dependent conversion rate is attributed to spin exchange between pairs of orthoexcitons. Implication of these results on the feasibility of Bose-Einstein condensation of paraexcitons in Cu(2)O is discussed.