After the stock market crash of October 19, 1987, interest in nonlinear dynamics and chaotic dynamics have increased in the field of financial analysis. The extent that the daily return data from the Shanghai Stock Exchange Index and the Shenzhen Stock Exchange Index exhibit non-random, nonlinear and chaotic characteristics are investigated by employing various tests from chaos theory. The Hurst exponent in R/S analysis rejects the hypothesis that the index return series are random, independent and identically distributed. The BDS test provides evidence for nonlinearity. The estimated correlation dimensions provide evidence for deterministic chaotic behaviors.