Centriole positioning is a key step in establishment and propagation of cell geometry, but the mechanism of this positioning is unknown. The ability of pre-existing centrioles to induce formation of new centrioles at a defined angle relative to themselves suggests they may have the capacity to transmit spatial information to their daughters. Using three-dimensional computer-aided analysis of cell morphology in Chlamydomonas, we identify six genes required for centriole positioning relative to overall cell polarity, four of which have known sequences. We show that the distal portion of the centriole is critical for positioning, and that the centriole positions the nucleus rather than vice versa. We obtain evidence that the daughter centriole is unable to respond to normal positioning cues and relies on the mother for positional information. Our results represent a clear example of "cytotaxis" as defined by Sonneborn, and suggest that centrioles can play a key function in propagation of cellular geometry from one generation to the next. The genes documented here that are required for proper centriole positioning may represent a new class of ciliary disease genes, defects in which would be expected to cause disorganized ciliary position and impaired function.