  The doubly charmed exotic state $T_{cc}$ recently discovered by the LHCb
Collaboration could well be a $DD^{*}$ molecular state long predicted in
various theoretical models, in particular, the $DD^*$ isoscalar axial vector
molecular state predicted in the one-boson-exchange model. In this work, we
study the $DDD^*$ system in the Gaussian Expansion Method with the $DD^*$
interaction derived from the one-boson-exchange model and constrained by the
precise binding energy of $273\pm63$ keV of $T_{cc}$ with respect to the
$D^{*+}D^0$ threshold. We show the existence of a $DDD^*$ state with a binding
energy of a few hundred keV and spin-parity $1^-$. Its main decay modes are
$DDD\pi$ and $DDD\gamma$. The existence of such a state could in principle be
confirmed with the upcoming LHC data and will unambiguously determine the
nature of the $T_{cc}^+$ state and of the many exotic state of similar kind,
thus deepening our understanding of the non-perturbative strong interaction.
