The 1.24-km base line vector between the two antennas of the Haystack Observatory was determined from X band radio interferometric observations of extragalactic sources via a new method that utilizes the precision inherent in fringe phase measurements. This method was employed in 11 separate experiments distributed between October 1974 and January 1976, each being between about 5 and 20 hours in duration. The rms scatters about the means for the veritcal and the two horizontal components of the base line obtained from the 11 independent determinations were 7.5, and 3 mm, respectively. The corresponding scatter for the base line length was 3 mm; the mean differed from the result obtained in a conventional survey by 8 mm, well within the 20-mm uncertainty of the survey. (The determination of the direction from the survey was too crude to be useful.) Another external check on our data was possible, since the azimuth and elevation axes of one of the antennas do not intersect but are separated by 318 mm. We estimated this horizontal offset from the radio interferometry data and found a difference of 10¿9 mm from the directly measured value, the relatively large rms scatter being due to the ~0.96 correlation between the estimate of this offset and that of the vertical component of the base lines. Use of a newly completed calibration system in future experiments should allow the scatter to be reduced to the millimeter level in all coordinates for short base lines. For long base lines, such repeatability should be degraded only to about the centimeter level if calibrated observations with sufficient sensitivity are made simultaneously at two frequency bands. An assessment of the accuracy of either our present or future base line results awaits the availability of an accepted, more accurate, standard for comparison. Nonetheless, base line changes can be determined reliably at any established level of repeatability.