We report the discovery of multiple condensations in the prestellar core candidate SMM 1A in the R Corona Australis cloud, which may represent the earliest phase of core fragmentation observed thus far. The separation between the condensations is between 1000 and 2100 AU, and their masses range from about 0.1 to 0.2 M☉. We find that the three condensations have extremely low bolometric luminosities (<0.1 L☉) and temperatures (<20 K), indicating that these are young sources that have yet to form protostars. We suggest that these sources were formed through the fragmentation of an elongated prestellar core. Our results, in concert with other observed protostellar binary systems with separations in the scale of 1000 AU, support the scenario that prompt fragmentation in the isothermal collapse phase is an efficient mechanism for wide binary star formation, while the fragmentation in the subsequent adiabatic phase may be an additional mechanism for close (≤100 AU) binary star formation.