We demonstrate for the first time that the theological parameters like the apparent viscosities and the first and second normal stress differences of suspensions of orientable particles can show chaotic behavior when the orientation vector evolves chaotically. We also demonstrate that the range of the values of the theological parameters is about 10000 times greater when the parameters evolve chaotically. This suggests that a wide range of properties may be obtained by small variations in controllable parameters. When coupled with suitable control of chaos algorithms, a wide range of suspension behavior is thus possible since a chaotic solution can be considered as an unlimited reservoir of periodic solutions of arbitrary period.