Abstract: The B+ -> D+K+pi(-) decay is observed in a data sample corresponding to 3.0 fb(-1) of pp collision data recorded by the LHCb experiment during 2011 and 2012. The signal significance is 8 sigma and the branching fraction is measured to be B(B+ -> D+K+pi(-)) = (5.31 +/- 0.90 +/- 0.48 +/- 0.35) x 10(-6), where the uncertainties are statistical, systematic and due to the normalization mode B+ -> D-K+pi(+), respectively. The Dalitz plot appears to be dominated by broad structures. Angular distributions are exploited to search for quasi-two-body contributions from B+ -> D*(2)(2460)K-0(+) and B+ -> (D+K*)(892)(0) decays. No significant signals are observed and upper limits are set on their branching fractions.