Precise positioning of the mitotic spindle is important for specifying the plane of cell division, which in turn determines how the cytoplasmic contents of the mother cell are partitioned into the daughter cells, and how the daughters are positioned within the tissue. During metaphase in the early C. elegans embryo, the spindle is aligned and centered on the anterior-posterior axis by a microtubule-dependent machinery that exerts restoring forces when the spindle is displaced from the center. To investigate the accuracy and stability of centering, we tracked the position and orientation of the mitotic spindle during the first cell division with high temporal and spatial resolution. We found that the precision is remarkably high: the cell-to-cell variation in the transverse position of the center of the spindle during metaphase, as measured by the standard deviation, was only 1.5% of the length of the short axis of the cell. Spindle position is also very stable: the standard deviation of the fluctuations in transverse spindle position during metaphase was only 0.5% of the short axis of the cell. Assuming that stability is limited by number fluctuations, we infer that the centering machinery has a large number of independent force-generating units, on the order of one thousand, consistent with the several thousand of astral microtubules in these cells. Astral microtubules grow out from the two spindle poles, contact and push against the cell cortex, and then shrink back shortly thereafter. The high stability of centering can be accounted for quantitatively if the astral microtubules buckle as they exert compressive, pushing forces onto the cortex. We thus propose that the large number of microtubules in the asters provides a highly precise mechanism for positioning the spindle while its assembly is completed during metaphase prior to the onset of anaphase.