We present the first observation of the decay B+→ρ+K0, using a data sample of 348fb-1 collected at the Υ(4S) resonance with the BABAR detector. The branching fraction and charge asymmetry are measured to be (8.0-1.3+1.4±0.6)×10-6 and (-12.2±16.6±2.0)%, respectively, where the first uncertainty is statistical and the second is systematic. The charge asymmetry is defined by Ach=(ΓB - ΓB+)/(ΓB-+ΓB+) with ΓB± the B± decay rate. The significance of the observed branching fraction, including systematic uncertainties, is 7.9 standard deviations. © 2007 The American Physical Society.