In the quest for a precise determination of the smallest CKM matrix element, $|V_{ub}|$, the decay $B \to \rho\,\ell\,\bar{\nu}$ offers a promising route to resolving the discrepancy between exclusive and inclusive determinations. This talk will outline our progress on a lattice QCD calculation of the $B \to \rho\,\ell\,\bar{\nu}$ form factors, where the $\rho$ resonance is treated as an enhancement in P-wave $\pi\pi$ scattering. After discussing the main computational hurdles, I will present details of our calculation and results obtained on a gauge ensemble with 2+1 dynamical quarks at a pion mass of approximately 320 MeV.
