A pair of triply charmed baryons, Ω_{ccc}Ω_{ccc}, is studied as an ideal dibaryon system by (2+1)-flavor lattice QCD with nearly physical light-quark masses and the relativistic heavy-quark action with the physical charm quark mass. The spatial baryon-baryon correlation is related to their scattering parameters on the basis of the HAL QCD method. The Ω_{ccc}Ω_{ccc} in the ^{1}S_{0} channel, taking into account the Coulomb repulsion with the charge form factor of Ω_{ccc}, leads to the scattering length a_{0}^{C}≃-19 fm and the effective range r_{eff}^{C}≃0.45 fm. The ratio r_{eff}^{C}/a_{0}^{C}≃-0.024, whose magnitude is considerably smaller than that of the dineutron (-0.149), indicates that Ω_{ccc}Ω_{ccc} is located in the unitary regime.