The performance of the maximum likelihood estimator for a 1-D chaotic signal in white Gaussian noise is derived. It is found that the estimator is inconsistent and therefore the usual asymptotic distribution (large data record length) is invalid. However, for high signal-to-noise ratios (SNR\u27s), the maximum likelihood estimator is asymptotically unbiased and attains the Cramér-Rao lower bound (CRLB). © 1995 IEE