The first measurement of the inclusive cross section for top quark pairs (tt‾) produced in association with two additional charm jets is presented. The analysis uses the dileptonic final states of tt‾ events produced in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 41.5fb−1, recorded by the CMS experiment at the LHC. A new charm jet identification algorithm provides input to a neural network that is trained to distinguish among tt‾ events with two additional charm (tt‾cc‾), bottom (tt‾bb‾), and light-flavour or gluon (tt‾LL) jets. By means of a template fitting procedure, the inclusive tt‾cc‾, tt‾bb‾, and tt‾LL cross sections are simultaneously measured, together with their ratios to the inclusive tt‾ + two jets cross section. This provides measurements of the tt‾cc‾ and tt‾bb‾ cross sections of 10.1±1.2(stat)±1.4(syst)pb and 4.54±0.35(stat)±0.56(syst)pb, respectively, in the full phase space. The results are compared and found to be consistent with predictions from two different matrix element generators with next-to-leading order accuracy in quantum chromodynamics, interfaced with a parton shower simulation.