The correlation dimension was used in this paper as a quantifier to describe the chaotic behavior of sleep EEG recorded from the hippocampus of adult rats during vigilance states of quiet-waking, slow-wave sleep, and REM sleep. A modified Grassberger-Procaccia method was implemented to compute the correlation integral using a Euclidean distance normalized by the embedding dimension. The performance of the correlation dimension as a measure to characterize the sleep EEG was compared to the quantitative measures derived from linear autoregressive models. Even though linear and chaotic measures are based on completely different theories and concepts, our experimental results have indicated them both effective in capturing the characteristic differences of sleep EEG during various states. The preliminary results have also shown the correlation dimension being particularly effective in emphasizing the differences in regard to the chaotic behavior between the EEG activity in SWS and QW and REM sleep.