It would appear both Chrono Cross and Final Fantasy Origins will be coming to the PlayStation Network as PSOne classics (for the PlayStation 3 and PlayStation Portable). Both titles have already been released on the PSN in Japan on July 6 and June 24 respectively.
Sony also mistakenly announced recently that both Chrono Trigger and Final Fantasy VI were being released on the PSN for the week starting September 19. They have since retracted this announcement and advised that no date is available for either title in the United States3. Chrono Trigger is already available on the Nintendo DS and Virtual Console and Final Fantasy VI is out on the PSN already in both Japan and Europe.
[source=http://www.esrb.org/ratings/search.jsp?title=chrono+cross ESRB - Chrono Cross ↩
[source=http://www.esrb.org/ratings/search.jsp?title=final+fantasy+origins ESRB - Final Fantasy Origins ↩