  The $B^+ \to D^{*-}K^+\pi^+$ decay potentially provides an excellent way to
investigate charm meson spectroscopy. The decay is searched for in a sample of
proton-proton collision data collected with the LHCb detector at centre-of-mass
energies of 7 and 8 TeV, corresponding to an integrated luminosity of $3~{\rm
fb}^{-1}$. A clear signal is observed, and the ratio of its branching fraction
to that of the $B^+ \to D^{*-}\pi^+\pi^+$ normalisation channel is measured to
be \begin{equation*}
  \frac{\mathcal{B}(B^+ \to D^{*-}K^+\pi^+)}{\mathcal{B}(B^+ \to
D^{*-}\pi^+\pi^+)} = \left( 6.39 \pm 0.27 \pm 0.48 \right) \times 10^{-2} \, ,
\end{equation*} where the first uncertainty is statistical and the second is
systematic. This is the first observation of the $B^+ \to D^{*-}K^+\pi^+$
decay.
