The essence of nuclear fusion is that energy can be released by the rearrangement of nucleons between the initial-and final-state nuclei. The recent discovery(1) of the first doubly charmed baryon Xi(++)(cc), which contains two charm quarks (c) and one up quark (u) and has a mass of about 3,621 megaelectronvolts (MeV) (the mass of the proton is 938 MeV) also revealed a large binding energy of about 130 MeV between the two charm quarks. Here we report that this strong binding enables a quark-rearrangement, exothermic reaction in which two heavy baryons (Lambda(c)) undergo fusion to produce the doubly charmed baryon Xi(++)(cc) and a neutron n (Lambda(c)Lambda(c) -> Xi(++)(cc) n), resulting in an energy release of 12 MeV. This reaction is a quark-level analogue of the deuterium-tritium nuclear fusion reaction (DT -> He-4 n). The much larger binding energy (approximately 280 MeV) between two bottom quarks (b) causes the analogous reaction with bottom quarks (Lambda(b)Lambda(b) -> Xi(0)(bb) n) to have a much larger energy release of about 138 MeV. We suggest some experimental setups in which the highly exothermic nature of the fusion of two heavy-quark baryons might manifest itself. At present, however, the very short lifetimes of the heavy bottom and charm quarks preclude any practical applications of such reactions.