A 900-day observation of the line profile of the unusual 1667 MHz OH maser in the bipolar nebula OH 231.8+4.2 has indicated that it varies sinusoidally by a factor of about 3, with a period of 684 + or - 40 days. This is in agreement with recent IR observations. The phase of the variations varies strongly with velocity. By interpreting phase differences in terms of the line-of-sight light travel time, the emission at each of 15 velocity intervals was assigned a relative line-of-sight distance. The overall, 70-day phase lag across the profile implies that this is one of the largest circumstellar masers, with a radius of at least 6000 AU, and that the source is expanding, since the redshifted emission has the greatest phase lag and is thus on the far side of the source. This data, together with maps previously made of OH 231.8+4.2 with the VLA at a number of velocities within the 1667 MHz line profile, reveals the three-dimensional structure of the maser. This structure agrees with the qualitative model previously suggested on the basis of VLA data alone.