Using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb-1, recorded by the LHCb detector at center-of-mass energies of 7 and 8 TeV, the Bc+→D0K+ decay is observed with a statistical significance of 5.1 standard deviations. By normalizing to B+→D¯ 0 π+ decays, a measurement of the branching fraction multiplied by the production rates for Bc+ relative to B+ mesons in the LHCb acceptance is obtained, RD0K=(fc/fu)×B (Bc+→D0K+)=(9. 3-2.5+2.8±0.6 )×10-7 , where the first uncertainty is statistical and the second is systematic. This decay is expected to proceed predominantly through weak annihilation and penguin amplitudes, and is the first Bc+ decay of this nature to be observed.