We present model calculations to fit the evolution of the intensity and profile of the [O I] λλ6300, 6364 emission doublet observed in the spectrum of SN 1987A. The fact that the doublet ratio R = F(6300)/F(6364) < 3 is evidence that these lines are optically thick for t <~ 1 yr after outburst. From this, we infer that the oxygen is distributed in a clumpy fashion throughout the supernova envelope. We can fit the data with a three-zone model having 1.3 M_sun_ of oxygen distributed within a freely expanding sphere with a volume filling factor f ~ 0.1. The temperature of the oxygen changed from T ~ 4100 K at day 200 to T ~ 2900 K at day 500.