Experimental studies of the oscillatory chlorite oxidation of thiocyanate carried out in a continuous-flow stirred tank reactor reveal chemical chaos arising from a period-doubling route. Analysis of the observed aperiodicity in terms of time series, Fourier spectra, reconstructed attractors, Poincare sections, return maps, and generalized Renyi dimensions confirms the deterministic nature of the chaotic behavior in this system. Under different experimental conditions, complex periodic states consisting of various combinations of large- and small-amplitude oscillations are observed, and aperiodic states intervene the complex periodic regions. Diversity in the aperiodic behaviors found in the chlorite-sulfur subfamily of chemical oscillators is discussed in a comparison of its chaotic constitutents.