Ciliates exhibit an asymmetry in arrangement of surface structures around the cell which could be termed handedness. If the usual order of placement of structures defines a ‘right-handed’ (RH) cell, then a cell with this order reversed would be ‘left-handed’ (LH). Such LH forms appear to be produced in Tetrahymena thermophila through aberrant reorganization of homopolar doublets back to the singlet condition. Four clones of LH forms were selected and subjected to genetic analysis to test whether this drastic phenotypic alteration resulted from a nuclear genetic change. The results of this analysis indicate that the change in handedness is not due to a genetic change in either the micronucleus or macronucleus. The LH form can, under certain circumstances, revert to the RH form, but typically it propagates itself across both vegetative and sexual generations with similar fidelity. While this analysis does not formally rule out certain possibilities of nuclear genic control involving regulatory elements transmitted through the cytoplasm, when the circumstances of origin and propagation of the LH condition are taken into account direct cortical perpetuation seems far more likely. Here we outline a conceptual framework centred on the idea of longitudinally propagated positional information; the positive evidence supporting this idea as well as further application of the idea itself are presented in the accompanying paper.