We have measured the transport properties of high-quality quantum wires fabricated in GaAs-AlGaAs by using cleaved edge overgrowth. The low temperature conductance is quantized as the electron density in the wire is varied. While the values of the conductance plateaus are reproducible, they deviate from multiples of the universal value of ${2e}^{2}/h$ by as much as 25%. As the temperature or dc bias increases the conductance steps approach the universal value. Several aspects of the data can be explained qualitatively using Luttinger liquid theory although there remain major inconsistencies with such an interpretation.