Materials described by the constitutive equations D=&egr;E+β&egr;∇¿E and B=μH+βμ∇¿H lack inversion symmetry due to chirality or handedness in their microstructure. In this paper, we describe the first direct measurements of the material properties &egr;, μ, and β for microwave chiral composite materials prepared in our laboratory in the frequency range of 8--40 GHz. We have used both reflection and transmission measurements for normally incident, linearly polarized plane waves in a specially designed free-space facility using spot focusing antennas. Different concentrations of the chiral inclusions in the form of miniature metallic springs that are left-handed only, right-handed only or equally mixed (racemic) have been studied. It is shown that &egr; and μ are comparable for all three samples at a given concentration, but β has equal but opposite values for the left- and right-handed samples, whereas it is nearly zero for the equichiral sample. The values of β thus obtained are compared to estimated values for suspensions of naturally occurring chiral molecules. The accuracy of the measurements is assessed by using the experimental procedure and inversion algorithm for standard materials like quartz. A new technique involving time domain repines has been used to remove the ambiguity that is usually encountered in the inversion of measured S parameters.