Old Chinese is essentially different from Modern Chinese, in both grammar and morphology. While there has recently been a great deal of work  on part-of-speech (POS) tagging for modern Chinese, the POS of Old Chinese is largely neglected. To the best of our knowledge, this is the first work in this area. Fortunately however, in terms of tagging, Old Chinese is easier than modern Chinese in that most Old Chinese words are single-character-formed, requiring no segmentation. So in this paper, we will propose and analyze a simple statistical approach for POS tagging of Old Chinese. We first designed a tagset for Old Chinese that is later shown to be accurate and efficient. Then we apply the hidden markov model (HMM) together with the Viterbi algorithm and made several improvements, such as sparse data problem handling, and unknown word guessing, both designed especially for Chinese. As the training set grows larger, the hit rate for bigram and trigram increases to 94.9% and 97.6%, respectively. The importance of our work lies in the  previously unseen features that are special for Old Chinese and we have developed successful techniques to deal with them. Although Old Chinese is now a dead language, this work still has many applications in such areas as Ancient-Modern Chinese Machine Translation.