Molecular gas freeze-out in the pre-stellar core L1689B

C(17)O J = 2 --> 1 observations have been carried out towards the pre-stellar core L1689B. By comparing the relative strengths of the hyperfine components of this line, the emission is shown to be optically thin. This allows accurate CO column densities to be determined and, for reference, this calculation is described in detail. The hydrogen column densities that these measurements imply are substantially smaller than those calculated from SCUBA dust emission data. Furthermore, the C(17)O J = 2 --> 1 column densities are approximately constant across L1689B, whereas the SCUBA column densities are peaked towards the centre. The most likely explanation is that CO is depleted from the central regions of L1689B. Simple models of pre-stellar cores with an inner depleted region are compared with the results. This enables the magnitude of the CO depletion to be quantified and also allows the spatial extent of the freeze-out to be firmly established. We estimate that within about 5000 au of the centre of L1689B, over 90 per cent of the CO has frozen on to grains. This level of depletion can only be achieved after a duration that is at least comparable to the free-fall time-scale.