  We compute theoretical predictions for the production of a W-boson in
association with a bottom-quark pair at hadron colliders at
next-to-next-to-leading order (NNLO) in QCD, including the leptonic decay of
the W-boson, while treating the bottom quark as massless. This calculation
constitutes the very first $2 \to 3$ process with a massive external particle
to be studied at such a perturbative order. We derive an analytic expression
for the required two-loop five-particle amplitudes in the leading colour
approximation employing finite-field methods. Numerical results for the cross
section and differential distributions are presented for the Large Hadron
Collider at $\sqrt{s} = 8$ TeV. We observe an improvement of the perturbative
convergence for the inclusive case and for the prediction with a jet veto upon
the inclusion of the NNLO QCD corrections.
