  The LHCb Collaboration, using its full data set from runs $1$ and $2$,
announced in $2019$ a surprising update of the hidden-charm pentaquark states
$P_c(4380)^+$ and $P_c(4450)^+$, observed in 2015. A new state, $P_c(4312)^+$,
was clearly seen at lower energies; furthermore, the original $P_c(4450)$
resonance was resolved into two individual states, named the $P_c(4440)^+$ and
the $P_c(4457)^+$. Motivated by the fact that these new hidden-charm pentaquark
states were successfully predicted by our chiral quark model, we extend herein
such study to the doubly charmed sector. The analyzed total spin and parity
quantum numbers are $J^P=\frac12^-$, $\frac32^-$ and $\frac52^-$, in the
$I=\frac12$ and $\frac32$ isospin channels. We find several possible narrow
baryon-meson resonances (theoretical masses in parenthesis): $IJ^P = \frac12
\frac12^-$ $\Sigma_c D(4356)$, $\frac12 \frac32^-$ $\Sigma^*_c D(4449)$,
$\frac32 \frac12^-$ $\Sigma_c D(4431)$, $\frac32 \frac12^-$ $\Sigma_c D(4446)$,
$\frac32 \frac32^-$ $\Sigma_c D^*(4514)$ and $\frac32 \frac52^-$ $\Xi^*_{cc}
\rho(4461)$ whose widths are $4.8$, $8.0$, $2.6$, $2.2$, $4.0$ and
$3.0\,\text{MeV}$, respectively. Moreover, one shallow bound-state is found,
too, with quantum numbers $IJ^P = \frac12 \frac32^-$ $\Xi^*_{cc} \pi(3757)$.
These doubly charmed pentaquark states are expected to be identified in future
experiments.
