The development of dating with radiocarbon (14C) by W. F. Libby and his colleagues, and its immediate application to archaeological objects from Mexico, aroused the interest of Mexican archaeological community, especially from the Prehistory Direction of the INAH. Joining efforts, the Institute of Physic of UNAM and INAH set up the first 14C laboratory in 1954. Augusto Moreno, who had worked and learned the technique with Libby in Chicago, was named the researcher in charge of this laboratory. We present the chronology of the project to install the first 14C laboratory in Mexico and some of the archaeological research projects that used the 14C dating technique carried out in Mexico in the 1960s.