As a precious cultural heritage of human beings, classical Chinese poetry has a very unique writing style and often contains special words that rarely appear in general Chinese texts, posting critical challenges for natural language processing. Little effort has been made in the literature for processing texts from classical Chinese poetry. This study fills in this gap with TopWORDS-Poetry, an unsupervised method that can achieve reliable text segmentation and word discovery for classical Chinese poetry simultaneously without pre-given vocabulary or training corpus. Experimental studies confirm that TopWORDS-Poetry can successfully recognize unique poetry words, such as named entities and literary allusions, from metrical poems of Complete Tang Poetry and segment these poetry lines into sequences of meaningful words with high quality.