Only a handful of massive starless core candidates have been discovered so far, but none of them have been fully confirmed. Within the MM1 clump in the filamentary infrared dark cloud G34.43+0.24 that was covered by the Atacama Large Millimeter/submillimeter Array (ALMA) ATOMS survey at Band 3 (∼2″, 6000 au) and the ALMA-QUARKS survey at Band 6 (∼0.″3, 900 au), two prestellar core candidates MM1-C and E1 with masses of 71 and 20 M _⊙ and radii of 2100–4400 au were discovered. The two cores show no obvious sign of star formation activities. In particular, MM1-C is a very promising massive prestellar core candidate with a total gas mass of 71 M _⊙ . Within MM1-C, we detected two extremely dense substructures, C1 and C2, as characterized by their high densities of ${n}_{{{\rm{H}}}_{2}}\sim {10}^{8\mbox{--}9}\,{\mathrm{cm}}^{-3}$ . Moreover, evidence of further fragmentation in C2 was also revealed. We have detected the primordial fragmentation in the earliest stage of massive star formation, and we speculate that MM1-C would be the birthplace of a massive multiple system. However, we cannot fully rule out the possibility that the massive prestellar core MM1-C will just form a cluster of low-mass stars if it undergoes further fragmentation.