Helical polymers appended with paired structurally different enantiomers, which have opposing helical sense preferences, yield a new kind of relationship between optical activity and temperature, and also reveal unusual details of the nature of chiral interactions. Consistent with a statistical physical theory developed for these experiments, the proportion of the competing chiral groups, determined by synthesis, fixes the compensation temperature at which the helical senses are equally populated. The lyotropic liquid crystal state formed by these polymers yields therefore a nematic state at any chosen temperature over a very wide range, with a cholesteric state arising with tightening pitch as temperature deviates from this point. Far from the nematic temperature, the pitch reaches the nanometer scale and therefore the reflection of visible light. Before crossing zero at the nematic temperature, the optical activity becomes so large that it may be observed with the unaided eye through crossed polarizers.