The optical, electronic and mechanical properties of synthetic and biological materials consisting of polymer chains depend sensitively on the conformation adopted by these chains. The range of conformations available to such systems has accordingly been of intense fundamental as well as practical interest, and distinct conformational classes have been predicted, depending on the stiffness of the polymer chains and the strength of attractive interactions between segments within a chain. For example, flexible polymers should adopt highly disordered conformations resembling either a random coil or, in the presence of strong intrachain attractions, a so-called 'molten globule'. Stiff polymers with strong intrachain interactions, in contrast, are expected to collapse into conformations with long-range order, in the shape of toroids or rod-like structures. Here we use computer simulations to show that the anisotropy distribution obtained from polarization spectroscopy measurements on individual poly[2-methoxy-5-(2'-ethylhexyl)oxy-1,4-phenylenevinylene] polymer molecules is consistent with this prototypical stiff conjugated polymer adopting a highly ordered, collapsed conformation that cannot be correlated with ideal toroid or rod structures. We find that the presence of so-called 'tetrahedral chemical defects', where conjugated carbon-carbon links are replaced by tetrahedral links, divides the polymer chain into structurally identifiable quasi-straight segments that allow the molecule to adopt cylindrical conformations. Indeed, highly ordered, cylindrical conformations may be a critical factor in dictating the extraordinary photophysical properties of conjugated polymers, including highly efficient intramolecular energy transfer and significant local optical anisotropy in thin films.