Using results on the mass gap in the sine-Gordon model combined withthe exact amplitudes in the bosonized representation of the Heisenbergspin-1/2 chain and one-loop renormalization group, we derive aquantitative expression for the gap in a dimerized spin-1/2chain. This expression is shown to be in good agreement with recentnumerical estimates when a marginallyirrelevant perturbation is taken into account.