We present the first studies of decays of the type B → DX, where D represents a charmed meson (D 0 , D ( * )+ or D s ) from the LHCb experiment at CERN. Our studies use data accumulated during the first months of the 2010 run of the LHC. This work represents the first steps on a programme towards a precision measurement of the angle γ of the CKM Unitarity Triangle. The prospects for this γ measurement are reviewed.