The tension between different determinations of the CKM matrix element Vub using measurements of either exclusive or inclusive semileptonic decays represents a long-standing puzzle in flavour physics. To resolve this, measurements of new exclusive channels as well as more precise measurements are needed. This thesis presents the first measurement of the exclusive semileptonic decay B+ -> rho0 mu+ nu at the LHCb experiment, using data collected during 2018. Profiting from the large number of B mesons produced in pp collisions at the LHC, a precise measurement of the B+ -> rho0 mu+ nu differential branching fraction as a function of the dilepton invariant mass squared is performed relative to the decay B+ -> D0 mu+ nu with D0 -> pi+ pi-. This measurement will be used to obtain a determination of the Vub matrix element from the signal channel. All steps leading to the final measurement are documented and the current precision of the result is given, with the numerical values of the result still kept blind to avoid accidental biases before the final publication.
The measurement presented in this thesis does not only pave the way for obtaining Vub, but also for measuring the full differential branching fraction that expresses the rich helicity structure of the B+ -> rho0 mu+ nu decay and provides more variables to test the Standard Model and to probe new physics.