  A study of prompt charm-hadron pair production in proton-lead collisions at
$\sqrt{s_\mathrm{NN}}= 8.16$ TeV is performed using data corresponding to an
integrated luminosity of about 30 nb${}^{-1}$, collected with the LHCb
experiment. Production cross-sections for different pairs of charm hadrons are
measured and kinematic correlations between the two charm hadrons are
investigated. This is the first measurement of associated production of two
charm hadrons in proton-lead collisions. The results confirm the predicted
enhancement of double parton scattering production in proton-lead collisions
compared to the single parton scattering production.
