  We calculate the leading-order matrix element for the decay $B \to K^*
\gamma$ in the quenched approximation of lattice QCD on a $24^3 \times 48$
lattice at $\beta=6.2$, using an O(a)-improved fermion action. Extrapolating
the quark masses to their physical values we obtain an on-shell form factor of
$T_1(q^2=0)=0.15+12-14$, where the errors quoted are purely statistical. We
find $T_1$ is approximately independent of the spectator quark mass and extract
$T_1(q^2=0)=0.15+5-4$ if this independence is assumed. We compare this with the
same form factor derived (in the Standard Model) from the CLEO experimental
branching ratio of $BR(B \to K^* \gamma) = (4.5 \pm 1.5 \pm 0.9) \times
10^{-5}$ and find the results to be consistent within statistical errors.
