  We consider a congruence of null geodesics in the presence of a quantized
spacetime metric. The coupling to a quantum metric induces fluctuations in the
congruence; we calculate the change in the area of a pencil of geodesics
induced by such fluctuations. For the gravitational field in its vacuum state,
we find that quantum gravity contributes a correction to the null Raychaudhuri
equation which is of the same sign as the classical terms. We thus derive a
quantum-gravitational focusing theorem valid for linearized quantum gravity.
