  We analyze the radiative leptonic $B_c$ decay mode: $B_c \to \ell \nu \gamma$
($\ell=e, \mu$) using a QCD-inspired constituent quark model. The prediction:
${\cal B}(B_c \to \ell \nu \gamma)\simeq 3 \times 10^{-5}$ makes this channel
experimentally promising in view of the large number of $B_c$ mesons which are
expected to be produced at the future hadron facilities.
