The observation of the decay B+→ψ(3770)K+, where the ψ(3770) was constructed in the D0D̄0 and D+D- decay channels, was reported. The branching fraction for the decay was measured and a 90% confidence level upper limit was set for the decay. Data was collected at the Y(4S) resonance by the Belle detector at the KEKB asymmetric-energy e+e- collider. Candidate π0 mesons were identified as pairs of non-charged-track-associated electromagnetic calorimeter clusters.