  This article presents the first measurement of the interaction between charm
hadrons and nucleons. The two-particle momentum correlations of $\mathrm{pD^-}$
and $\mathrm{\overline{p}D}^+$ pairs are measured by the ALICE Collaboration in
high-multiplicity pp collisions at $\sqrt{s} = 13~\mathrm{TeV}$. The data are
compatible with the Coulomb-only interaction hypothesis within
(1.1-1.5)$\sigma$. The level of agreement slightly improves if an attractive
nucleon(N)$\overline{\mathrm{D}}$ strong interaction is considered, in contrast
to most model predictions which suggest an overall repulsive interaction. This
measurement allows for the first time an estimation of the 68% confidence level
interval for the isospin $\mathrm{I}=0$ inverse scattering length of the
$\mathrm{N\overline{D}}$ state ${f_{0,~\mathrm{I}=0}^{-1} \in
[-0.4,0.9]~\mathrm{fm^{-1}}}$, assuming negligible interaction for the isospin
$\mathrm{I}=1$ channel.
