  A Dalitz plot analysis of $B^0 \to \eta_c(1S) K^+\pi^-$ decays is performed
using data samples of $pp$ collisions collected with the LHCb detector at
centre-of-mass energies of $\sqrt{s}=7,~8$ and $13$ TeV, corresponding to a
total integrated luminosity of $4.7~\text{fb}^{-1}$. A satisfactory description
of the data is obtained when including a contribution representing an exotic
$\eta_c(1S) \pi^-$ resonant state. The significance of this exotic resonance is
more than three standard deviations, while its mass and width are $4096 \pm
20~^{+18}_{-22}$ MeV and $152 \pm 58~^{+60}_{-35}$ MeV, respectively. The
spin-parity assignments $J^P=0^+$ and $J^{P}=1^-$ are both consistent with the
data. In addition, the first measurement of the $B^0 \to \eta_c(1S) K^+\pi^-$
branching fraction is performed and gives $\displaystyle \mathcal{B}(B^0 \to
\eta_c(1S) K^+\pi^-) = (5.73 \pm 0.24 \pm 0.13 \pm 0.66) \times 10^{-4}$, where
the first uncertainty is statistical, the second systematic, and the third is
due to limited knowledge of external branching fractions.
