The $B^{-}to D^{+}K^{-}pi^{-}$ decay is observed in a data sample corresponding to $3.0~rm{fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. Its branching fraction is measured to be ${cal B}(B^{-}to D^{+}K^{-}pi^{
-}) = (7.31 pm 0.19 pm 0.22 pm 0.39) times 10^{-5}$ where the uncertainties are statistical, systematic and from the branching fraction of the normalisation channel $B^{-}to D^{+}pi^{-}pi^{-}$, respectively. An amplitude analysis of the resonant structure of the $B^{-}to D^{+}K^{-}pi^{-}$ decay is used to measure the contributions from quasi-two-body $B^{-}to D_{0}^{*}(2400)^{0}K^{-}$, $B^{-}to D_{2}^{*}(2460)^{0}K^{-}$, and $B^{-}to D_{J}^{*}(2760)^{0}K^{-}$ decays, as well as from nonresonant sources. The $D_{J}^{*}(2760)^{0}$ resonance is determined to have spin~1.
