  We study triple-parton scattering effects in open charm production in
proton-proton collisions at the LHC. Predictions for one, two and three $c\bar
c$ pairs production are given for $\sqrt{s}= 7$ TeV and $\sqrt{s}= 13$ TeV.
Quite large cross sections, of the order of milibarns, for the triple-parton
scattering mechanism are obtained. We suggest a measurement of three $D^{0}$ or
three $\bar{D^{0}}$ mesons by the LHCb collaboration. The predicted visible
cross sections are of the order of a few nanobarns. The counting rates
including $D^{0} \to K^{-}\pi^{+}$ branching fractions are also given. We
predict that at $\sqrt{s}= 13$ TeV a few thousands of events of triple-$D^{0}$
production can be observed by the LHCb collaboration.
